相关论文: Integration over the Pauli quantum group

The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…

A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter…

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The…

We study the integrability of Poisson and Dirac structures that arise from quotient constructions. From our results we deduce several classical results as well as new applications. We also give explicit constructions of Lie groupoids…

A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…

Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…

We formulate the canonical structure of Yang--Mills theory in terms of Poisson brackets of gauge invariant observables analogous to Wilson loops. This algebra is non--trivial and tractable in a light--cone formulation. For U(N) gauge…

Using methods of computer algebra, especially Gr\"obner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous)…

Associated to a finite graph $X$ is its quantum automorphism group $G(X)$. We prove a formula of type $G(X*Y)=G(X)*_wG(Y)$, where $*_w$ is a free wreath product. Then we discuss representation theory of free wreath products, with the…

In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a…

We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…

Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum…

We present a novel approach to generate Bessel-Gauss modes of arbitrary integer order and well-defined optical angular momentum in a gradient index medium of transverse parabolic profile. The propagation and coherence properties, as well as…

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…

$C^*$-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is…

The Lie-Rinehart algebra of a manifold M, defined by the Lie structure of the vector fields, their action and their module structure on the infinitely differentiable functions on M, is a common, diffeomorphism invariant, algebra for both…

In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…