arXiv subjects

T. Kopf

Publications and source records attributed to T. Kopf.

6 recordsLinked to original sources

arXiv2007

Generally covariant quantum mechanics on noncommutative configuration spaces

We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. We give a detailed account of several examples, e.g., of nonabelian Yang-Mills theories, and of noncommutative tori. Moreover we, examine models over the Moyal-deformed plane. Assuming the conservation of electrical charges, we show that in this case the canonical uncertainty relation [x_k, \dot{x}_l] = ig_{kl} with metric g_{kl} is only consistent if g_{kl} is constant.

math-ph↗

arXiv2004

Algebra generators and information theory

A general simplicity problem in category theory is proposed. A particular example, the simplest choice of generators of an algebra is specified and illustrated by an example.

math.RA↗

arXiv2000

A Spectral Quadruple for de Sitter Space

A set of data supposed to give possible axioms for spacetimes with a sufficient number of isometries in spectral geometry is given. These data are shown to be sufficient to obtain 1+1 dimensional de Sitter spacetime. The data rely at the moment somewhat on the guidance given by a required symmetry, in part to allow explicit calculations in a specific model. The framework applies also to the noncommutative case. Finite spectral triples are discussed as an example.

math-ph↗

arXiv2000

Spectral geometry of spacetime

Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier. Here, it is proposed to use the Hadamard condition of quantum field theory as a smoothness principle.

hep-th↗

arXiv1998

Spinorial density matrix equation and gauge covariance

In this work we apply the Lie group representation method introduced in the real time formalism for finite-temperature quantum-field theory, thermofield dynamics, to derive a spinorial density matrix equation. Symmetry properties of such equation are analysed, and as a basic result it is shown that one solution is the generalised density matrix operator proposed by Heinz, to deal with gauge covariant kinetic equations. In the same context, preliminary aspects of a Lagrangian formalism to derive kinetic equations, as well as quantum density matrix equations in curved space-time, are discussed.

hep-th↗

arXiv1996

Thermal Field Dynamics and Bialgebras

In Thermal Field Dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenberg bialgebra. No artificial redefinitions of fields are necessary to obtain the thermal representations and the case of arbitrary dimension is considered from the beginning. Our results support a possibly fundamental role of bialgebra structures in defining a general framework for Thermal Field Dynamics.

hep-th↗