Locally gauge-invariant formulation of parastatistics

A locally gauge-invariant formulation of parastatistics, which is equivalent to a Yang-Mills gauge theory, is given, using a complex Clifford algebra (case of SU(N)) or a real Clifford algebra (case of SO(N)). In particular, for the SU(3) case, the gauged theory of para-Fermi quarks is equivalent to quantum chromodynamics.     

A manifestly gauge-invariant formulation of quantum electrodynamics

A manifestly gauge-invariant formulation of quantum electrodynamics is constructed in which the basic dynamical variables are physically observable quantities. The theory is relativistically covariant, because the structure of the Poincaré group is built into it from the beginning.     

The gravitational light shift and the Sachs-Wolfe effect

Using a 3+1 decomposition of spacetime, we derive a new formula to compute the gravitational light shifts as measured by two observers which are normal to the spacelike hypersurfaces defining the foliation. This formula is quite general and is also independent of the existence of Killing fields. Known examples are considered to illustrate the usefulness of the formula. In particular, we focus on the Sachs-Wolfe effect that arises in a perturbed Friedman-Robertson-Walker cosmology.     

Covariant formulation of non-equilibrium statistical thermodynamics

The Fokker Planck equation is considered as the master equation of macroscopic fluctuation theories. The transformation properties of this equation and quantities related to it under general coordinate transformations in phase space are studied. It is argued that all relations expressing physical properties should be manifestly covariant, i.e. independent of the special system of coordinates used. The covariance of the Langevin-equations and the Fokker Planck equation is demonstrated. The diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space. Covariant drift vectors associated to the Langevin- and the Fokker Planck equation are found. It is shown that special coordinates exist in which the covariant drift vector of the Fokker Planck equation and the usual non-covariant drift vector are equal.The physical property of detailed balance and the equivalent potential conditions are given in covariant form. Finally, the covariant formulation is used to study how macroscopic forces couple to a system in a non-equilibrium steady state. A general fluctuation-dissipation theorem for the linear response to such forces is obtained.     

Model-independent dark energy differentiation with the integrated Sachs-Wolfe effect

We study the integrated Sachs-Wolfe effect using a model-independent parametrization of the dark energy equation of state, w(z). Cosmic variance severely restricts the class of models distinguishable from one based on cold dark matter and a cosmological constant unless w(z) currently satisfies w(o)(Q)>-0.8, or exhibits a rapid, late-time, transition at redshifts z<3. Because of the degeneracy with other cosmological parameters, models with a slowly varying w(z) cannot be differentiated from each other or from a cosmological constant. This may place a fundamental limit on our understanding of the origin of the currently observed acceleration.     

Covariant formulation of BPS black holes and the scalar weak gravity conjecture

We find through a systematic analysis that all but 29,223 of the 473.8 million 4D reflexive polytopes found by Kreuzer and Skarke have a 2D reflexive subpolytope. Such a subpolytope is generally associated with the presence of an elliptic or genus one fibration in the corresponding birational equivalence class of Calabi-Yau threefolds. This extends the growing body of evidence that most Calabi-Yau threefolds have an elliptically fibered phase.     

Possibility of constructing a gauge-invariant quantum formulation for nongauge classical theory

A general method is proposed for the construction of a gauge-invariant canonical quantum formulation for the gauge-invariant classical theory that depends on the set of parameters. The conditions for closure of the algebra of operators, which generate quantum gauge transformations, entails constraints on the parameters of the theory. The approach described is demonstrated by the example of a closed bosonic string, interacting with a background tachyonic field. The condition of a mass shell for the tachyon is reproduced within the framework of the proposed canonical formulation. Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–24, June, 1997.     

Covariant and consistent anomalies in two dimensions in path-integral formulation

We give a definition of a one-parameter family of regularized chiral currents in a chiral non-Abelian gauge theory in two dimensions in path-integral formulation. We show that covariant and consistent currents are obtained from this family by selecting two specific values of the free parameter, and thus our regularization interpolates between these two. Our procedure uses chiral bases constructed from eigenfunctions of thesame operator for defining _L and . Definition of integration measure and regularization is done in terms of thesame Hermitian operator . Covariant and consistent currents (and indeed the entire family) are classically conserved. Difference with previous works are explained, in particular, that anomaly in a general basis does differ from the Jacobian contribution.     

A relation between gauge-invariant formulation of QCD and string theory in two dimensions

We have studied the explicit relation between the gauge-invariant path-ordered operator (POO) and a string field in two dimensions. For this purpose, we use the hamiltonian of two-dimensional quantum chromodynamics reformulated in terms of POO. POO is expanded in a power series of a non-local bosonic operator. We show that such a bosonic operator describes Bars and Hanson's free string field in the second quantization. Interactions among bosonic operators are treated in perturbation theory. The coupling constant is proportional to 1/√N_c.     

Covariant formulation of the dynamics in a dissipative quantum dielectric obtained from a simplified Lagrangian

Equations of motion and energy-momentum tensors are obtained for a dissipative medium sustaining electromagnetic polarizations using a Lagrangian formalism. A previous work has been simplified by reducing the number of independent vector fields interacting with the sink modes. A relativistic formalism of the same is also suggested.     

Duality and the phases of massive gauge-invariant QCD

I discuss the phase structure of massive gauge invariant QCD (the gauged non-linear sigma model) using an operator formalism proposed by 't Hooft. The dual variables for this system are determined and the 't Hooft loop operator is constructed from these dual field variables. Its equal time commutation relations with the Wilson loop operator is explicitly verified. The system possesses two possible phases. In the semi-classical approximation (weak coupling), magnetic confinement as indicated by an area law for the expectation value of 't Hooft loops is observed. If above a certain critical coupling a condensate of vortices is formed, then the expectation value of the 't Hooft loop in the dilute vortex approximation shows a perimeter law indicating electric confinement.     

Torsion and gauge-invariant massive electrodynamics

We study electrodynamics in Einstein-Cartan space-time, that is, in space-time with torsion, and show an analogy with the Chern-Simons gauge-invariant massive electrodynamics. In our case, however, there is no arbitrary parameter, the torsionQ playing the role of the Chern-Simons parameter. This leads to bounds on the photon mass, charge, and torsion coupling.     

Construction of a gauge-invariant cutoff of quantum electrodynamics from a non-local gauge-invariant Lagrangian

A non-local gauge-invariant Lagrangian is given, which describes gauge-invariant quantum electro-dynamics with a modified fermion propagator. Some examples are discussed.