arXiv subjects

Bernd Kuckert

Publications and source records attributed to Bernd Kuckert.

10 recordsLinked to original sources

arXiv2005

Spin, Statistics, and Reflections, II. Lorentz Invariance

The analysis of the relation between modular P$_1$CT-symmetry -- a consequence of the Unruh effect -- and Pauli's spin-statistics relation is continued. The result in the predecessor to this article is extended to the Lorentz symmetric situation. A model $\G_L$ of the universal covering $\widetilde{L_+^\uparrow}\cong SL(2,\complex)$ of the restricted Lorentz group $L_+^\uparrow$ is modelled as a reflection group at the classical level. Based on this picture, a representation of $\G_L$ is constructed from pairs of modular P$_1$CT-conjugations, and this representation can easily be verified to satisfy the spin-statistics relation.

math-ph↗

arXiv2005

Spin, Statistics, and Reflections, I. Rotation Invariance

The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry, which is referred to as "modular P_1CT-symmetry (Bisognano, Wichmann, 1975, 1976, and Guido, Longo, [funct-an/9406005]). This symmetry is used to construct a representation of G_R by pairs of modular P_1CT-operators. The representation thus obtained satisfies Pauli's spin-statistics relation.

hep-th↗

arXiv2004

Spin & Statistics in Nonrelativistic Quantum Mechanics, II

Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.

quant-ph↗

arXiv2003

Spin & Statistics in Nonrelativistic Quantum Mechanics, I

A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J the total (i.e., spin plus orbital) angular momentum of a single particle, and denote by j the total angular momentum of the corresponding two-particle system with respect to its center of mass. In three spatial dimensions, write J_z and j_z for the z-components of these vector operators. In two spatial dimensions, the spin statistics connection holds if and only if there exists a unitary operator U such that j=2UJU^*. In three dimensions, the analogous relation cannot hold as it stands, but restricting it to an appropriately chosen subspace of the state space yields a sufficient and necessary condition for the spin-statistics connection.

quant-ph↗

arXiv2002

Moving Quantum Systems: Particles Versus Vacuum

We give an overview on a couple of recent results concerning the KMS-condition and the characterization of thermodynamic equilibrium states from a moving observer's point of view. These results include a characterization of vacuum states in relativistic quantum field theory and a general derivation of the Unruh effect.

math-ph↗

arXiv2001

$β$-Boundedness, Semipassivity, and the KMS-Condition

The proof of a recent result by Guido and Longo establishing the equivalence of the KMS-condition with complete $β$-boundedness is shortcut and generalized in such a way that a covariant version of the theorem is obtained.

math-ph↗

arXiv2001

Covariant Thermodynamics of Quantum Systems: Passivity, Semipassivity, and the Unruh Effect

According to the Second Law of Thermodynamics, cycles applied to thermodynamic equilibrium states cannot perform work (passivity property of thermodyamic equilibrium states). In the presence of matter this can hold only in the rest frame of the matter, as moving matter drives, e.g., windmills and turbines. If, however, a homogeneous and stationary state has the property that no cycle can perform more work than an ideal windmill, then it can be shown that there is some inertial frame where the state is a thermodynamic equilibrium state. This provides a covariant characterization of thermodynamic equilibrium states. In the absence of matter, cycles should perform work only when driven by nonstationary inertial forces caused by the observer's motion. If a pure state of a relativistic quantum field theory behaves this way, it satisfies the spectrum condition and exhibits the Unruh effect.

hep-th↗

arXiv2000

Localization Regions of Local Observables

Exploiting the properties of the Jost-Lehmann-Dyson representation, it is shown that in 1+2 or more spacetime dimensions, a nonempty smallest localization region can be associated with each local observable (except for the c-numbers) in a theory of local observables in the sense of Araki, Haag, and Kastler. Necessary and sufficient conditions are given that observables with spacelike separated localization regions commute (locality of the net alone does not yet imply this).

math-ph↗

arXiv1995

Borchers' Commutation Relations and Modular Symmetries

Recently Borchers has shown that in a theory of local observables, certain unitary and antiunitary operators, which are obtained from an elementary construction suggested by Bisognano and Wichmann, commute with the translation operators like Lorentz boosts and \pct-operators, respectively. We conclude from this that as soon as the operators considered implement {\em any} symmetry, this symmetry can be fixed up to at most some translation. As a symmetry, we admit any unitary or antiunitary operator under whose adjoint action any algebra of local observables is mapped onto an algebra which can be localized somewhere in Minkowski space.

hep-th↗

arXiv1994

A New Approach to Spin and Statistics

We give an algebraic proof of the spin-statistics connection for the parabosonic and parafermionic quantum topological charges of a theory of local observables with a modular PCT-symmetry. The argument avoids the use of the spinor calculus and also works in 1+2 dimensions. It is expected to be a progress towards a general spin-statistics theorem including also (1+2)-dimensional theories with braid group statistics.

hep-th↗