Related papers: Topologically inequivalent quantizations
By resorting to some results in quantum field theories with spontaneous breakdown of symmetry we show that an explanation based on microscopic dynamics can be given of the fact that topological defect formation is observed during the…
In the framework of the Closed-Time-Path formalism, we show how topological defects may arise in Quantum Field Theory as result of a localized (inhomogeneous) condensation of particles. We demonstrate our approach on two examples; kinks in…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We demonstrate a novel mechanism for the formation of topological defects in a first order phase transition for theories in the presence of small explicit symmetry breaking terms. We carry out numerical simulations of collisions of two…
(2+1) dimensional gravity is equivalent to an exactly soluble non-Abelian Chern-Simons gauge field theory (E Witten 1988). Regarding this as the topological phase of quantum gravity in (2+1)d, we suggest a topological symmetry breaking by…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
We investigate the topological defects in phenomenological models describing mixtures of charged condensates with commensurate electric charges. Such situations are expected to appear for example in liquid metallic deuterium. This is…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in…
Multi-gap superconductors exhibit interesting properties. In an $N$-gap superconductor, we have in general $U(1)^N$ phase invariance. This multiple-phase invariance is partially or totally spontaneously broken in a superconductor. The…
The GNS representation construction is considered in a general case of topological involutive algebras of quantum systems, including quantum fields, and inequivalent state spaces of these systems are characterized. We aim to show that, from…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
The problem of defining and constructing representations of the Canonical Commutation Relations can be systematically approached via the technique of {\it algebraic quantization}. In particular, when the phase space of the system is linear…
We construct an artificial U(1) gauge field in the cold atom system to form a monopole along with vortices. It is supposed that the cold atoms are confined on a spherical surface, and two sets of identical laser beams in the opposite…
In this work, we propose a topological quantum field theory phase for four-dimensional gravity. We show it is able to generate, not only General Relativity, but the whole family of Lovelock-Cartan theories of gravity. This is accomplished…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
Coherence vortices are screw-type topological defects in the phase of Glauber's two-point degree of quantum coherence, associated with pairs of spatial points at which an ensemble-averaged stochastic quantum field is uncorrelated. Coherence…
Topology in momentum space is the main characteristics of the ground states of a system at zero temperature, the quantum vacua. The gaplessness of fermions in bulk, on the surface or inside the vortex core is protected by topology.…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We establish a classical analog of the Nambu-Goldstone theorem for spontaneous breaking of spacetime symmetries. It provides a counting rule for independent Nambu-Goldstone fields and states which of them are gapped. We demonstrate that…