The Matsubara-Fradkin Thermodynamical Quantization of Podolsky Electrodynamics

In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's auxiliary field method to the quantization of the Podolsky electrodynamics in thermodynamic equilibrium. This approach allows us to write consistently the path integral representation for the partition function of gauge theories in a simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write the most general form for the polarization tensor in thermodynamic equilibrium.Comment: Submitted to Physical Review

Generating Functional for Gauge Invariant Actions: Examples of Nonrelativistic Gauge Theories

We propose a generating functional for nonrelativistic gauge invariant actions. In particular, we consider actions without the usual magnetic term. Like in the Born-Infeld theory, there is an upper bound to the electric field strength in these gauge theories.Comment: 14 pages, 2 figures; v2: misprints correcte

The wall of the cave

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang Mills theories must be described by the non-critical strings in the five dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang-Mills theories. The article is written on the occasion of the 40-th anniversary of the IHES.Comment: 18 pages, Late

On the pathwidth of almost semicomplete digraphs

We call a digraph {\em $h$-semicomplete} if each vertex of the digraph has at most $h$ non-neighbors, where a non-neighbor of a vertex $v$ is a vertex $u \neq v$ such that there is no edge between $u$ and $v$ in either direction. This notion generalizes that of semicomplete digraphs which are $0$-semicomplete and tournaments which are semicomplete and have no anti-parallel pairs of edges. Our results in this paper are as follows. (1) We give an algorithm which, given an $h$-semicomplete digraph $G$ on $n$ vertices and a positive integer $k$, in $(h + 2k + 1)^{2k} n^{O(1)}$ time either constructs a path-decomposition of $G$ of width at most $k$ or concludes correctly that the pathwidth of $G$ is larger than $k$. (2) We show that there is a function $f(k, h)$ such that every $h$-semicomplete digraph of pathwidth at least $f(k, h)$ has a semicomplete subgraph of pathwidth at least $k$. One consequence of these results is that the problem of deciding if a fixed digraph $H$ is topologically contained in a given $h$-semicomplete digraph $G$ admits a polynomial-time algorithm for fixed $h$.Comment: 33pages, a shorter version to appear in ESA 201

Volkov-Akulov theory and D-branes

The action of supersymmetric Born-Infeld theory (D-9-brane in a Lorentz covariant static gauge) has a geometric form of the Volkov-Akulov-type. The first non-linearly realized supersymmetry can be made manifest, the second world-volume supersymmetry is not manifest. We also study the analogous 2 supersymmetries of the quadratic action of the covariantly quantized D-0-brane. We show that the Hamiltonian and the BRST operator are build from these two supersymmetry generators.Comment: 10 pages, Latex, Contribution to Supersymmetry and Quantum Field Theory, International Seminar dedicated to the memory of D. V. Volkov (Kharkov, 1997