432 research outputs found
Continuous Histories and the History Group in Generalised Quantum Theory
We treat continuous histories within the histories approach to generalised
quantum mechanics. The essential tool is the `history group': the analogue,
within the generalised history scheme, of the canonical group of single-time
quantum mechanics.Comment: 25 page
Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace
Working with anticommuting Weyl(or Mayorana) spinors in the framework of the
van der Waerden calculus is standard in supersymmetry. The natural frame for
rigorous supersymmetric quantum field theory makes use of operator-valued
superdistributions defined on supersymmetric test functions. In turn this makes
necessary a van der Waerden calculus in which the Grassmann variables
anticommute but the fermionic components are commutative instead of being
anticommutative. We work out such a calculus in view of applications to the
rigorous conceptual problems of the N=1 supersymmetric quantum field theory.Comment: 14 page
Grobner Bases for Finite-temperature Quantum Computing and their Complexity
Following the recent approach of using order domains to construct Grobner
bases from general projective varieties, we examine the parity and
time-reversal arguments relating de Witt and Lyman's assertion that all path
weights associated with homotopy in dimensions d <= 2 form a faithful
representation of the fundamental group of a quantum system. We then show how
the most general polynomial ring obtained for a fermionic quantum system does
not, in fact, admit a faithful representation, and so give a general
prescription for calcluating Grobner bases for finite temperature many-body
quantum system and show that their complexity class is BQP
Comment on "Fermionic entanglement ambiguity in noninertial frames"
In this comment we show that the ambiguity of entropic quantities calculated
in Physical Review A 83, 062323 (2011) for fermionic fields in the context of
Unruh effect is not related to the properties of anticommuting fields, as
claimed in Physical Review A 83, 062323 (2011), but rather to wrong
mathematical manipulations with them and not taking into account a fundamental
superselection rule of quantum field theory.Comment: To appear in Physical Review A. Some of the problems discussed in
this comment can also be found in other previously published papers studying
the Unruh effect for fermions (in the context of quantum information theory).
An extended version of the comment can be found here
http://arxiv.org/abs/1108.555
Radion Induced Spontaneous Baryogenesis
We describe a possible scenario for the baryogenesis arising when matter is
added on the branes of a Randall-Sundrum model with a radion stabilizing
potential. We show that the radion field can naturally induce spontaneous
baryogenesis when the cosmological evolution for the matter on the branes is
taken into account.Comment: LaTeX 2e, 8 pages and no figures, minor corrections to match version
to appear in MPL
Massless scalar field in two-dimensional de Sitter universe
We study the massless minimally coupled scalar field on a two--dimensional de
Sitter space-time in the setting of axiomatic quantum field theory. We
construct the invariant Wightman distribution obtained as the renormalized
zero--mass limit of the massive one. Insisting on gauge invariance of the model
we construct a vacuum state and a Hilbert space of physical states which are
invariant under the action of the whole de Sitter group. We also present the
integral expression of the conserved charge which generates the gauge
invariance and propose a definition of dual field.Comment: 13 page
Remarks on some new models of interacting quantum fields with indefinite metric
We study quantum field models in indefinite metric. We introduce the modified
Wightman axioms of Morchio and Strocchi as a general framework of indefinite
metric quantum field theory (QFT) and present concrete interacting relativistic
models obtained by analytical continuation from some stochastic processes with
Euclidean invariance. As a first step towards scattering theory in indefinite
metric QFT, we give a proof of the spectral condition on the translation group
for the relativistic models.Comment: 13 page
Massless, String Localized Quantum Fields for Any Helicity
For any massless, irreducible representation of the covering of the proper,
orthochronous Poincar\'e group we construct covariant, free quantum fields that
generate the representation space from the vacuum and are localized in
semi-infinite strings in the sense of commutation or anti-commutation of the
field operators at space-like separation of the strings.Comment: Minor corrections. To be published in Journal of Mathematical Physic
A teleparallel model for the neutrino
The main result of the paper is a new representation for the Weyl Lagrangian
(massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e.
an orthonormal tetrad of covector fields. We write down a simple Lagrangian -
wedge product of axial torsion with a lightlike element of the coframe - and
show that variation of the resulting action with respect to the coframe
produces the Weyl equation. The advantage of our approach is that it does not
require the use of spinors, Pauli matrices or covariant differentiation. The
only geometric concepts we use are those of a metric, differential form, wedge
product and exterior derivative. Our result assigns a variational meaning to
the tetrad representation of the Weyl equation suggested by J.B.Griffiths and
R.A.Newing.Comment: 4 pages, REVTe
Space-time symplectic extension
It is conjectured that in the origin of space-time there lies a symplectic
rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1
instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the
space-time local structure group. A discrete sequence of the metric space-times
of the fixed dimensionalities d=(2l)^2 and signatures, with l(2l-1) time-like
and l(2l+1) space-like directions, defined over the set of the Hermitian
second-rank spin-tensors is considered as an alternative to the
pseudo-Euclidean extra dimensional space-times. The basic concepts of the
symplectic framework are developed in general, and the ordinary and
next-to-ordinary space-time cases with l=1,2, respectively, are elaborated in
more detail. In particular, the scheme provides the rationale for the
four-dimensionality and 1+3 signature of the ordinary space-time.Comment: 15 pp, LaTe
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