Related papers: A quantum Mermin--Wagner theorem for a generalized…
We construct, in classical two-time physics, the necessary structure for the most general configuration space formulation of quantum mechanics containing gravity in d+2 dimensions. This structure is composed of a symmetric Riemannian metric…
Physical states in quantum mechanics are rays in a Hilbert space. Projective representations of a relativity group transform between the quantum physical states that are in the admissible class. The physical observables of position, time,…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still can become non-Gibbsian. The mechanism rests on the…
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…
We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this…
A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels. We show that the coupled-channel…
We study a discrete dynamic on weighted bipartite graphs on a torus, analogous to dimer integrable systems in Goncharov-Kenyon 2013. The dynamic on the graph is an urban renewal together with shrinking all 2-valent vertices, while it is a…
Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary…
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…
2-Chern-Simons theory, or more commonly known as 4d BF-BB theory with gauged shift symmetry, is a natural generalization of Chern-Simons theory to 4-dimensional manifolds. It is part of the bestiary of higher-homotopy Maurer-Cartan…
In theoretical studies of two-dimensional (2D) systems, the Mermin-Wagner theorem prevents continuous symmetry breaking at any finite temperature, thus forbidding a Landau phase transition at a critical temperature $T_c$. The difficulty…
We propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac…
A theory has been presented previously in which the geometrical structure of a real four-dimensional space time manifold is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group. The group…
In this proceeding we consider a translation invariant Nelson type model in two spatial dimensions modeling a scalar relativistic particle in interaction with a massive radiation field. As is well-known, the corresponding Hamiltonian can be…
We extend our study of the field-theoretic description of matrix-vector models and the associated many-body problems of one dimensional particles with spin. We construct their Yangian-su(R) invariant Hamiltonian. It describes an interacting…
We prove the vertex-reinforced jump process (VRJP) is recurrent in two dimensions for any translation invariant finite range initial rates. Our proof has two main ingredients. The first is a direct connection between the VRJP and sigma…
A symmetry based quantization method of reparametrization invariant systems is described; it will work for all systems that possess complete sets of perennials whose Lie algebras close and which generate a sufficiently large symmetry…
Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows…
We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first…