Related papers: Introduction to the BV-BFV formalism
Lectures held at the 22nd "Saalburg" Summer School (2016)
We present a new collective field formalism with two rather than one collective field to derive the antifield formalism for extended BRST invariant quantisation. This gives a direct and physical proof of the scheme of Batalin, Lavrov and…
These notes are intended as an introduction to noncommutative (quantum) filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as the least squares…
We review the Schwinger-Keldysh, or in-in, formalism for studying quantum dynamics of systems out-of-equilibrium. The main motivation is to rephrase well known facts in the subject in a mathematically elegant setting, by exhibiting a set of…
In this overview article we present a formalism suitable for constructing models of QFT's on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the standard QFT…
In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…
A general field-antifield BV formalism for antisymplectic first class constraints is proposed. It is as general as the corresponding symplectic BFV-BRST formulation and it is demonstrated to be consistent with a previously proposed…
The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the…
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure…
This text aims to explains briefly the formalism of quantum mechanics to mathematicians.
We perform the gauge-fixing of the theory of a chiral two-form boson in six dimensions starting from the action given by Pasti, Sorokin and Tonin. We use the Batalin-Vilkovisky formalism, introducing antifields and writing down an extended…
This paper contains a revised version of the lecture notes of a short course on the quantization of gauge theories. Starting from a sketchy review of scattering theory, the paper describes the lines of BRST-Faddeev-Popov quantization…
In this Letter we consider the perturbative quantum gravity on the super-manifold which remains invariant under absolutely anticommuting BRST and anti-BRST transformations. In addition to that the theory posses one more symmetry known as…
The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in 2-dimensions. The charge corresponding to BRST symmetry derived from this…
In this book chapter, we provide a tutorial introduction to one-way quantum computation and many of the techniques one can use to understand it. The techniques which are described include the stabilizer formalism and the logical Heisenberg…
A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…
In this talk the main features of the operator formalism for the $b-c$ systems on general algebraic curves developed in refs. [1-2] are reviewed. The first part of the talk is an introduction to the language of algebraic curves. Some…
The widespread bra-ket formalism offers valuable tools for conducting representation-free considerations in quantum theory. However, it is not without its drawbacks. In this work, we discuss these drawbacks in detail and subsequently…
In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…
We apply newly improved Batalin-Fradkin-Tyutin Hamiltonian method to the chiral Schwinger Model in the case of the regularization ambiguity $a>1$. We show that one can systematically construct the first class constraints by the BFT…