Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrised field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary , in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrised field theory in order to analyse issues at...

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occu...

Cutwidth of a digraph is a width measure introduced by Chudnovsky, Fradkin, and Seymour [4] in connection with development of a structural theory for tournaments, or more generally, for semi-complete digraphs. In this paper we provide an algorithm with running time 2 √ k log k) · n that tests whether the cutwidth of a given n-vertex semi-complete digraph is at most k, improving upon the current...

Lattice Landau gauge and other related lattice gauge fixing schemes are known to violate spectral positivity. The most direct sign of the violation is the rise of the effective mass as a function of distance. The origin of this phenomenon lies in the quenched character of the auxiliary field g used to implement lattice gauge fixing, and is similar to quenched QCD in this respect. This is best s...

I point out an unexpected relation between the BV (Batalin–Vilkovisky) and the BFV (Batalin–Fradkin–Vilkovisky) formulations of the same pure gauge (topological) theory. The non-minimal sector in the BV formulation of the topological theory allows one to construct the Poisson bracket and the BRST charge on some Lagrangian submanifold of the BV configuration space; this Lagrangian submanifold ca...

The notions of cutwidth and pathwidth of digraphs play a central role in the containment theory for tournaments, or more generally semi-complete digraphs, developed in a recent series of papers by Chudnovsky, Fradkin, Kim, Scott, and Seymour [2, 3, 4, 8, 9, 11]. In this work we introduce a new approach to computing these width measures on semi-complete digraphs, via degree orderings. Using the ...

A bstract We propose a superspace formulation for conformal ( p , q ) supergravity in two dimensions as gauge theory of the superconformal group OSp 0 |2; ℝ × with flat connection. Upon degauging certain local symmetries, this is shown to reduce conformally SO( following properties: (i) its structure direct product Lorentz and ); (ii) residual scale symmetry realised by super-Weyl transformatio...

Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In classical theory, infinite-dimensional targets considered as well (this then encompasses also higher-dimensional theories in hamiltonian formalism). The properties Hamilton–Jacobi (HJ) action described details and several examples explicitly computed (including...

A two-dimensional nonrelativistic fermion system coupled to both electromagnetic gauge fields and Chern-Simons gauge fields is analysed. Polarization tensors relevant in the quantum Hall effect and anyon superconductivity are obtained as simple closed integrals and are evaluated numerically for all momenta and frequencies. The correction to the energy density is evaluated in the random phase ap...

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occu...