# Mathematical Physics

## New submissions

[ total of 44 entries: 1-44 ]
[ showing up to 2000 entries per page: fewer | more ]

### New submissions for Tue, 20 Mar 18

[1]
Title: Solutions of the $U_q(\widehat{\mathfrak{sl}}_N)$ reflection equations
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI)

We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm A}^{(1)}_{N-1}$. We also show that all invertible solutions can be obtained by an appropriate affinization procedure from solutions of the constant untwisted and twisted reflection equations.

[2]
Title: A Deal with the Devil: From Divergent Perturbation Theory to an Exponentially-Convergent Self-Consistent Expansion
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech)

For many nonlinear physical systems, approximate solutions are pursued by conventional perturbation theory in powers of the non-linear terms. Unfortunately, this often produces divergent asymptotic series, collectively dismissed by Abel as "an invention of the devil." An alternative method, the self-consistent expansion, has been introduced by Schwartz and Edwards. Its basic idea is a rescaling of the zeroth-order system around which the solution is expanded, to achieve optimal results. While low-order self-consistent calculations have been remarkably successful in describing the dynamics of non-equilibrium many-body systems (e.g., the Kardar-Parisi-Zhang equation), its convergence properties have not been elucidated before. To address this issue we apply this technique to the canonical partition function of the classical harmonic oscillator with a quartic $gx^{4}$ anharmonicity, for which perturbation theory's divergence is well-known. We explicitly obtain the $N^{\text{th}}$ order self-consistent expansion for the partition function, which is rigorously found to converge exponentially fast in $N$, and uniformly in $g$, for any coupling $g>0$. Comparing the self-consistent expansion with other methods that improve upon perturbation theory (Borel resummation, hyperasymptotics, Pad\'e approximants, and the Lanczos $\tau$-method), it compares favorably with all of them for small $g$ and dominates over them for large $g$. Remarkably, the self-consistent expansion is shown to successfully capture the correct partition function for the double-well potential case, where no perturbative expansion exists. Our treatment is generalized to the case of many oscillators, as well as to a more general nonlinearity of the form $g|x|^{q}$ with $q\ge0$ and complex $g$. These results allow us to treat the Airy function, and to see the fingerprints of Stokes lines in the self-consistent expansion.

[3]
Title: Asymptotic properties of integrals of quotients, when the numerator oscillates and denominator degenerates
Authors: Sergei Kuksin
Subjects: Mathematical Physics (math-ph)

We study asymptotical expansion as $\nu\to0$ for integrals over ${ \mathbb{R} }^{2d}=\{(x,y)\}$ of quotients of the form $F(x,y) \cos(\lambda x\cdot y) \big/ \big( (x\cdot y)^2+\nu^2\big)$, where $\lambda\ge 0$ and $F$ decays at infinity sufficiently fast. Integrals of this kind appear in the theory of wave turbulence.

[4]
Title: Toda type equations over multi-dimensional lattices
Subjects: Mathematical Physics (math-ph); Commutative Algebra (math.AC); Exactly Solvable and Integrable Systems (nlin.SI)

We introduce a class of recursions defined over the $d$-dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations satisfy the coprimeness property, which is one of integrability detectors analogous to the singularity confinement test. While the degree of their iterates grows exponentially, they exhibit pseudo-integrable nature in terms of the coprimeness property. We also prove that the equations can be expressed as mutations of a seed in the sense of the Laurent phenomenon algebra.

[5]
Title: Local martingales associated with SLE with internal symmetry
Authors: Shinji Koshida
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR); Quantum Algebra (math.QA); Representation Theory (math.RT)

We consider Schramm-Loewner evolutions with internal degrees of freedom that are associated with representations of affine Lie algebras, following the group theoretical formulation of SLE. We observe that SLEs considered by Bettelheim et al. [PRL 95, 251601 (2005)] and Alekseev et al. [Lett. Math. Phys. 97, 243-261 (2011)] in correlation function formulation are reconstrunced. We also explicitly write down stochastic differential equations on internal degrees of freedom for Heisenberg algebras and the affine $\mathfrak{sl}_{2}$. Our formulation enables to write down several local martingales associated with the solution of SLE from computation on a representation of an affine Lie algebra. Indeed, we write down local martingales associated with solution of SLE for Heisenberg algebras and the affine $\mathfrak{sl}_{2}$. We also find affine $\mathfrak{sl}_{2}$ symmetry of a space of SLE local martingales for the affine $\mathfrak{sl}_{2}$, which can be extended to other affine Lie algebras.

[6]
Title: The planar 3-body problem II:reduction to pure shape and spherical geometry (2nd version)
Subjects: Mathematical Physics (math-ph); Differential Geometry (math.DG)

Geometric reduction of the Newtonian planar three-body problem is investigated in the framework of equivariant Riemannian geometry, which reduces the study of trajectories of three-body motions to the study of their moduli curves, that is, curves which record the change of size and shape, in the moduli space of oriented mass-triangles. The latter space is a Riemannian cone over the shape 2-sphere, and the shape curve is the image curve on this sphere. It is shown that the time parametrized moduli curve is in general determined by the relative geometry of the shape curve and the shape potential function. This also entails the reconstruction of time, namely the geometric shape curve determines the time parametrization of the moduli curve, hence also the three-body motion itself, modulo a fixed rotation of the plane. The first version of this work is an (unpublished) paper from 2012, and the present version is an editorial revision of this.

[7]
Title: The correct formulation of Gleason's theorem in quaternionic Hilbert spaces
Authors: Valter Moretti, Marco Oppio (Trento U. and TIFPA-INFN)
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Operator Algebras (math.OA); Quantum Physics (quant-ph)

From the viewpoint of the theory of orthomodular lattices of elementary propositions, Quantum Theories can be formulated in real, complex or quaternionic Hilbert spaces as established in Sol\'er's theorem. The said lattice eventually coincides with the lattice of all orthogonal projectors on a separable Hilbert space over R, C, or over the algebra of quaternions H. Quantum states are $\sigma$-additive probability measures on that non-Boolean lattice. Gleason's theorem proves that, if the Hilbert space is separable with dimension >2 and the Hilbert space is either real or complex, then states are one-to-one with standard density matrices (self-adjoint, positive, unit-trace, trace-class operators). The extension of this result to quaternionic Hilbert spaces was obtained by Varadarajan in 1968. Unfortunately, even if the hard part of the proof is correct, the formulation of this extension is mathematically incorrect. This is due to some peculiarities of the notion of trace in quaternionic Hilbert spaces, e.g., basis dependence, making the theory of trace-class operators in quaternionic Hilbert spaces different from the standard theory in real and complex Hilbert spaces. A minor issue also affects Varadarajan's statement for real Hilbert space formulation. This paper is mainly devoted to present Gleason-Varadarajan's theorem into a technically correct form valid for the three types of Hilbert spaces. After having develped part of the general mathematical technology of trace-class operators in (generally non-separable) quaternionic Hilbert spaces, we prove that only the {\em real part} of the trace enters the formalism of quantum theories (also dealing with unbounded observables and symmetries) and it can be safely used to formulate and prove a common statement of Gleason's theorem.

[8]
Title: Exchanging the phase space and symmetry group of integrable Hamiltonian systems related to Lie bialgebra of bi-symplectic type
Subjects: Mathematical Physics (math-ph)

We construct integrable Hamiltonian systems with Lie bialgebra of bi-symplectic type for which the Poisson-Lie group $G$ plays the role of phase space and its dual Lie group $\tilde{G}$ plays the role of symmetry group of the system. We give the new transformation to exchange the role of phase space and symmetry group. We obtain relation between integrals of motion of these two integrable systems. Finally we give some examples about real four dimensional Lie bialgebras of bi-symplectic type.

[9]
Title: Kinematics and Dynamics of Quantum Walks in terms of Systems of Imprimitivity
Subjects: Mathematical Physics (math-ph)

We build systems of imprimitivity (SI) in the context of quantum walks and provide geometric constructions for their configuration space. We consider three systems, an evolution of unitaries from the group SO3 on a low dimensional de Sitter space where the walk happens on the dual of SO3, standard quantum walk whose SI live on the orbits of stabilizer subgroups (little groups) of semidirect products describing the symmetries of 1+1 spacetime, and automorphisms (walks are specific automorphisms) on distant-transitive graphs as application of the constructions.

### Cross-lists for Tue, 20 Mar 18

[10]  arXiv:1803.06476 (cross-list from quant-ph) [pdf, other]
Title: PT-symmetric phase transition, hysteresis and bound states in the continuum
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

We explicate the merging of levels and spectral bifurcation near an exceptional point as also the appearance of resonances and bound states in the PT-broken phase for the PT-symmetric complex Scarf II potential. The bound states in the PT-broken phase are manifested as spectral singularities and are found to be bound states in continuum and thus seen as zero width resonances, starting to first appear at the exceptional points. The intimate connection of PT-symmetry breaking and breaking of supersymmetry is pointed out as also the phenomenon of hysteresis near exceptional point. Intriguingly, the PT-symmetric Hamiltonians related by SUSY are also found to be isospectrally deformed counterparts for a specific parametric condition with the deformation satisfying the Korteweg-deVries equation.

[11]  arXiv:1803.06511 (cross-list from nlin.SI) [pdf, ps, other]
Title: On discretization of the Euler top
Authors: A.V. Tsiganov
Comments: 12 pages, 2 figures, LaTeX with AMS fonts
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Dynamical Systems (math.DS)

Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing the integrals of motion with the continuous time system and the Poisson bracket up to the integer scaling factor.

[12]  arXiv:1803.06584 (cross-list from nlin.SI) [pdf, ps, other]
Title: Linear Instability of the Peregrine Breather: Numerical and Analytical Investigations
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)

We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By constructing solutions of the linearization of the nonlinear Schr\"odinger equation in terms of quadratic products of components of the eigenfunctions of the Zakharov-Shabat system, we show that the Peregrine breather is linearly unstable. A numerical study employing a highly accurate Chebychev pseudo-spectral integrator confirms exponential growth of random initial perturbations of the Peregrine breather.

[13]  arXiv:1803.06592 (cross-list from math.RT) [pdf, ps, other]
Title: Layer structure of irreducible Lie algebra modules
Authors: Jorgen Rasmussen
Subjects: Representation Theory (math.RT); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Combinatorics (math.CO)

Let $\mathfrak{g}$ be a finite-dimensional simple complex Lie algebra. A layer sum is introduced as the sum of formal exponentials of the distinct weights appearing in an irreducible $\mathfrak{g}$-module. It is argued that the character of every finite-dimensional irreducible $\mathfrak{g}$-module admits a decomposition in terms of layer sums, with only non-negative integer coefficients. Ensuing results include a new approach to the computation of Weyl characters and weight multiplicities, and a closed-form expression for the number of distinct weights in a finite-dimensional irreducible $\mathfrak{g}$-module. The latter is given by a polynomial in the Dynkin labels, of degree equal to the rank of $\mathfrak{g}$.

[14]  arXiv:1803.06717 (cross-list from math.AP) [pdf, other]
Title: High frequency limits for invariant Ruelle densities
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Dynamical Systems (math.DS); Spectral Theory (math.SP)

We establish an equidistribution result for Ruelle resonant states on compact locally symmetric spaces of rank one. More precisely, we prove that among the first band Ruelle resonances there is a density one subsequence such that the respective products of resonant and co-resonant states converge weakly to the Liouville measure. We prove this result by establishing an explicit quantum-classical correspondence between eigenspaces of the scalar Laplacian and the resonant states of the first band of Ruelle resonances which also leads to a new description of Patterson-Sullivan distributions.

[15]  arXiv:1803.06728 (cross-list from math.PR) [pdf, ps, other]
Title: A non-intersecting random walk on the Manhattan lattice and SLE_6
Authors: Tom Kennedy
Subjects: Probability (math.PR); Mathematical Physics (math-ph)

We consider a random walk on the Manhattan lattice. The walker must follow the orientations of the bonds in this lattice, and the walker is not allowed to visit a site more than once. When both possible steps are allowed, the walker chooses between them with equal probability. The walks generated by this model are known to be related to interfaces in a certain percolation model. So it is natural to conjecture that the scaling limit is SLE$_6$. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.

[16]  arXiv:1803.06764 (cross-list from hep-th) [pdf, other]
Title: Exact holographic RG flows and the $A_{1}\times A_{1}$ Toda chain
Comments: latex, 55 pages, 34 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)

We construct analytic solutions of Einstein gravity coupled to a dilaton field with a potential given by a sum of two exponentials, by rewriting the equations of motion in terms of an integrable Toda chain. Such solutions can be interpreted as domain walls interpolating between different asymptotics, and as such they can have interesting applications in holography. In some cases we can find flows that start from an AdS fixed point. We also find analytic black brane solutions at finite temperature. We discuss the properties of the solutions and the interpretation in terms of RG flow.

[17]  arXiv:1803.06829 (cross-list from cond-mat.stat-mech) [pdf, ps, other]
Title: Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Probability (math.PR)

We consider current statistics for a two species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green's function as well as for a joint current distribution of the model, and study its long time behavior. For a step type initial condition, we show that the limiting distribution is a product of the Gaussian and the GUE Tracy-Widom distribution. This is the first analytic confirmation for a multi-component system of a prediction from the recently proposed non-linear fluctuating hydrodynamics for one dimensional systems.

[18]  arXiv:1803.06840 (cross-list from math.RA) [pdf, ps, other]
Title: On n-Hom-Leibniz algebras and cohomology
Subjects: Rings and Algebras (math.RA); Mathematical Physics (math-ph); Quantum Algebra (math.QA)

The purpose of this paper is to provide a cohomology of $n$-Hom-Leibniz algebras. Moreover, we study some higher operations on cohomology spaces and deformations.

[19]  arXiv:1803.06857 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Anomalous heat equation in a system connected to thermal reservoirs
Comments: Main text: 5 pages. Supplementary: 9 page. 5 Figures
Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD)

We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as well as in the non-stationary state where the later describes the relaxation to the steady state. In contrast to the Fourier heat equation in the diffusive case, here we show that the evolution of the temperature profile is governed by a non-local anomalous heat equation. We provide numerical verifications of our results.

[20]  arXiv:1803.06901 (cross-list from math.RT) [pdf, ps, other]
Title: Cyclic Sieving and Cluster Duality for Grassmannian
Subjects: Representation Theory (math.RT); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Combinatorics (math.CO)

We introduce a decorated configuration space $\mathscr{C}onf_n^\times(a)$ with a potential function $\mathcal{W}$. We prove the cluster duality conjecture of Fock-Goncharov for Grassmannians, that is, the tropicalization of $(\mathscr{C}onf_n^\times(a), \mathcal{W})$ canonically parametrizes a linear basis of the homogenous coordinate ring of the Grassmannian ${\rm Gr}_a(n)$. We prove that $(\mathscr{C}onf_n^\times(a), \mathcal{W})$ is equivalent to the mirror Landau-Ginzburg model of Grassmannian considered by Marsh-Rietsch and Rietsch-Williams. As an application, we show a cyclic sieving phenomenon involving plane partitions under a sequence of piecewise-linear toggles.

[21]  arXiv:1803.06938 (cross-list from hep-th) [pdf, other]
Title: Conformal amplitude hierarchy and the Poincare disk
Journal-ref: J. Phys.: Conf. Ser. 965 (2018) 012036
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

The amplitude for the singlet channels in the 4-point function of the fundamental field in the conformal field theory of the 2d $O(n)$ model is studied as a function of $n$. For a generic value of $n$, the 4-point function has infinitely many amplitudes, whose landscape can be very spiky as the higher amplitude changes its sign many times at the simple poles, which generalize the unique pole of the energy operator amplitude at $n=0$. In the stadard parameterization of $n$ by angle in unit of $\pi$, we find that the zeros and poles happen at the rational angles, forming a hierarchical tree structure inherent in the Poincar\'{e} disk. Some relation between the amplitude and the Farey path, a piecewise geodesic that visits these zeros and poles, is suggested. In this hierarchy, the symmetry of the congruence subgroup $\Gamma(2)$ of $SL(2,\mathbb{Z})$ naturally arises from the two clearly distinct even/odd classes of the rational angles, in which one respectively gets the truncated operator algebras and the logarithmic 4-point functions.

[22]  arXiv:1803.06970 (cross-list from math.DG) [pdf, ps, other]
Title: Higher symmetries of symplectic Dirac operator
Comments: Symplectic Dirac operator, Higher symmetry algebra, Projective differential geometry, Minimal nilpotent orbit, $\mathfrak{sl}(3,\mR)$
Subjects: Differential Geometry (math.DG); Mathematical Physics (math-ph); Functional Analysis (math.FA); Representation Theory (math.RT); Symplectic Geometry (math.SG)

We construct in projective differential geometry of the real dimension $2$ higher symmetry algebra of the symplectic Dirac operator ${D}\kern-0.5em\raise0.22ex\hbox{/}_s$ acting on symplectic spinors. The higher symmetry differential operators correspond to the solution space of a class of projectively invariant overdetermined operators of arbitrarily high order acting on symmetric tensors. The higher symmetry algebra structure corresponds to a completely prime primitive ideal having as its associated variety the minimal nilpotent orbit of $\mathfrak{sl}(3,{\mathbb{R}})$.

### Replacements for Tue, 20 Mar 18

[23]  arXiv:1506.00563 (replaced) [pdf, other]
Title: Rational degeneration of M-curves, totally positive Grassmannians and KP2-solitons
Comments: 49 pages, 10 figures. Minor revisions
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
[24]  arXiv:1611.09680 (replaced) [pdf, ps, other]
Title: Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
Authors: Shin Hayashi
Comments: v3: section 4 added, references and typos corrected. 15 pages, 1 figure
Subjects: Mathematical Physics (math-ph); K-Theory and Homology (math.KT)
[25]  arXiv:1706.01354 (replaced) [pdf, ps, other]
Title: Non Projected Calabi-Yau Supermanifolds over $\mathbb{P}^2$
Comments: 17 pages. Exposition of the main theorem improved. Typos fixed
Subjects: Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[26]  arXiv:1706.01822 (replaced) [pdf, other]
Title: Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation
Comments: Published version, 7 pages, 2 figures
Subjects: Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph)
[27]  arXiv:1706.04629 (replaced) [pdf, other]
Title: Verification Studies for the Noh Problem using Non-ideal Equations of State and Finite Strength Shocks
Comments: 14 pages, 7 figures, 19 images
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Engineering, Finance, and Science (cs.CE); Mathematical Physics (math-ph)
[28]  arXiv:1706.09130 (replaced) [pdf, other]
Title: Potts models with a defect line
Subjects: Mathematical Physics (math-ph); Probability (math.PR)
[29]  arXiv:1707.00977 (replaced) [pdf, ps, other]
Title: Electric-Magnetic Aspects On Yang-Mills Fields
Authors: Tosiaki Kori
Subjects: Symplectic Geometry (math.SG); Mathematical Physics (math-ph); Differential Geometry (math.DG)
[30]  arXiv:1707.04963 (replaced) [pdf, other]
Title: A large class of solvable multistate Landau-Zener models and quantum integrability
Comments: The 2nd version contains considerable changes, including new sections, that are based on recent advances in arXiv/1711.09945 (new Ref.[1])
Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph)
[31]  arXiv:1707.05351 (replaced) [pdf, ps, other]
Title: The reduced phase space of Palatini-Cartan-Holst theory
Comments: Corrected a minor mistake and reformulated some of the results. Main theorem restructured and overall improvements. 26 pages
Subjects: Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); Symplectic Geometry (math.SG)
[32]  arXiv:1708.02487 (replaced) [pdf, ps, other]
Title: Spectral density of mixtures of random density matrices for qubits
Comments: 21 pages, LaTex, 6 figures
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)
[33]  arXiv:1709.03364 (replaced) [pdf, other]
Title: Detecting localized eigenstates of linear operators
Subjects: Numerical Analysis (math.NA); Mathematical Physics (math-ph); Spectral Theory (math.SP)
[34]  arXiv:1709.09226 (replaced) [pdf, ps, other]
Title: Second quantized quantum field theory based on invariance properties of locally conformally flat space-times
Authors: John Mashford
Comments: 50 pages, version for submission to journal. Minor modifications including adding a reference
Subjects: Mathematical Physics (math-ph)
[35]  arXiv:1710.04965 (replaced) [pdf, ps, other]
Title: Lorentz signature and twisted spectral triples
Comments: minor corrections. To be published in JHEP
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
[36]  arXiv:1710.09542 (replaced) [pdf, ps, other]
Title: Differential operators on the algebra of densities and factorization of the generalized Sturm-Liouville operator
Subjects: Mathematical Physics (math-ph)
[37]  arXiv:1710.10481 (replaced) [pdf, ps, other]
Title: Quantum Newton duality
Subjects: Mathematical Physics (math-ph)
[38]  arXiv:1711.00778 (replaced) [pdf, other]
Title: Asymptotic behaviour of a network of oscillators coupled to thermostats of finite energy
Authors: Andrey V. Dymov
Comments: 22 pages. In comparison with the previous version where a chain of oscillators was considered, the result is generalized to the case when the oscillators form arbitrary network
Subjects: Mathematical Physics (math-ph); Dynamical Systems (math.DS)
[39]  arXiv:1711.05450 (replaced) [pdf, ps, other]
Title: Scattering Theory and $\mathcal{P}\mathcal{T}$-Symmetry
Comments: Slightly expanded revised version, 38 pages
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optics (physics.optics)
[40]  arXiv:1803.00332 (replaced) [pdf, other]
Title: Geometry Transition in Covariant Loop Quantum Gravity
Comments: PhD thesis submitted for the degree of Doctor in Theoretical and Mathematical Physics. Defended at the Center for Theoretical Physics/CNRS/Aix-Marseille University, the 23rd of October 2017. The manuscript is written in English and begins with a short summary in French
Subjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
[41]  arXiv:1803.04913 (replaced) [pdf, other]
Title: On non-commutativity in quantum theory (I): from classical to quantum probability
Authors: Luca Curcuraci
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR)
[42]  arXiv:1803.04916 (replaced) [pdf, other]
Title: On non-commutativity in quantum theory (II): toy models for non-commutative kinematics
Authors: Luca Curcuraci