Hydrodynamics in an external field

The methods of statistical dynamics are applied to a fluid with 5 conserved fields (the mass, the energy, and the three components of momentum) moving in a given external potential. When the potential is zero, we recover a previously derived system of parabolic differential equations, called "corrections to fluid dynamics".Comment: extends results of math-ph/0105013 in the presence of an external field; to appear in Rep. Math. Phys. (2002

On Birkhoff's theorem for doubly stochastic completely positive maps of matrix algebras

AbstractA study is made of the extreme points of the convex set of doubly stochastic completely positive maps of the matrix algebra Mn. If n = 2 the extreme points are precisely the unitary maps, but if n ⩾ 3 there are nonunitary extreme points, examples of which are exhibited. A tilde operation is defined on the linear maps of Mn and used to give an elementary derivation of a result of Kummerer and Maassen

The quantum information manifold for epsilon-bounded forms

Let H be a self-adjoint operator bounded below by 1, and let V be a small form perturbation such that RVS has finite norm, where R is the resolvent at zero to the power 1/2 +epsilon, and S is the resolvent to the power 1/2-epsilon. Here, epsilon lies between 0 and 1/2. If the Gibbs state defined by H is sufficiently regular, we show that the free energy is an analytic function of V in the sense of Frechet, and that the family of density operators defined in this way is an analytic manifold modelled on a Banach space.Comment: 12 pages, report to Torun Conference, 199

QCD recursion relations from the largest time equation

We show how by reassembling the tree level gluon Feynman diagrams in a convenient gauge, space-cone, we can explicitly derive the BCFW recursion relations. Moreover, the proof of the gluon recursion relations hinges on an identity in momentum space which we show to be nothing but the Fourier transform of the largest time equation. Our approach lends itself to natural generalizations to include massive scalars and even fermions.Comment: 18 pages, 2 figures, minor changes to Sect.

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

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

Perturbative Quantum Field Theory at Positive Temperatures: An Axiomatic Approach

It is shown that the perturbative expansions of the correlation functions of a relativistic quantum field theory at finite temperature are uniquely determined by the equations of motion and standard axiomatic requirements, including the KMS condition. An explicit expression as a sum over generalized Feynman graphs is derived. The canonical formalism is not used, and the derivation proceeds from the beginning in the thermodynamic limit. No doubling of fields is invoked. An unsolved problem concerning existence of these perturbative expressions is pointed out.Comment: 17pages Late

CP violation in the effective action of the Standard Model

Following a suggestion by Smit, the CP odd terms of the effective action of the Standard Model, obtained by integration of quarks and leptons, are computed to sixth order within a strict covariant derivative expansion approach. No other approximations are made. The final result so derived includes all Standard Model gauge fields and Higgs. Remarkably, at the order considered in this work, all parity violating contributions turn out to be zero. Non vanishing CP violating terms are obtained in the C-odd P-even sector. These are several orders of magnitude larger than perturbative estimates. Various unexpected regularities in the final result are noted.Comment: 32 pages, no figures. Section added. To appear in JHE

Relativity and EPR Entanglement: Comments

Recent experiment by Zhinden et al (Phys. Rev {\bf A} 63 02111, 2001) purports to test compatibility between relativity and quantum mechanics in the classic EPR setting. We argue that relativity has no role in the EPR argument based solely on non-relativistic quantum formalism. It is suggested that this interesting experiment may have significance to address fundamental questions on quantum probability.Comment: 6 pages, no figure; Submitted to Phys. Rev.