相关论文: The Charge Quantum Numbers of Gauge Invariant Quas…
A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…
Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schr\"{o}dinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can…
We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a $\kappa$-deformed scalar…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
In the presence of spacetime boundaries, diffeomorphisms in gravitational theories can become physical and acquire non-vanishing Noether charges. These charges obey an algebra which, within the extended phase-space formalism, faithfully…
Quantum Electrodynamics can be formulated as the theory of an antisymmetric tensor gauge field. In this formulation the topological current of this field appears as an additional source for the electromagnetic field. The topological charge…
The recently-developed techniques of Noether analysis of the quantum-group spacetime symmetries of some noncommutative field theories rely on the {\it ad hoc} introduction of some peculiar auxiliary transformation parameters, which appear…
Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of…
We study the Fock description of a quantum free field on the three-sphere with a mass that depends explicitly on time, also interpretable as an explicitly time dependent quadratic potential. We show that, under quite mild restrictions on…
SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with "twisted" boundary conditions,…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…
In the setting of geometric quantization, we associate to any prequantum bundle automorphism a unitary map of the corresponding quantum space. These maps are controlled in the semiclassical limit by two invariants of symplectic topology:…
We begin a study of the representation theory of quantum continuous $\mathfrak{gl}_\infty$, which we denote by $\mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of…
Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field…
This paper clarifies the local structure of the energy representation of a local gauge group. The group to be considered is a smooth map from a manifold into a compact Lie group. It acts on a Boson Fock spaces generated by connection…
The quantum theory of U(1) connections admits a diffeomorphism invariant representation in which the electric flux through any surface is quantized. This representation is the analog of the representation of quantum SU(2) theory used in…
Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…