Related papers: Computing the BRST Operator Used in Quantization o…
Using the quantum construction of the BV-BFV method for perturbative gauge theories, we show that the obstruction for quantizing a codimension 1 theory is given by the second cohomology group with respect to the boundary BRST charge.…
We propose a new BRST-like quantization procedure which is applicable to dynamical systems containing both first and second class constraints. It requires no explicit separation into first and second class constraints and therefore no…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
Lagrange multipliers are present in any gauge theory. They possess peculiar gauge transformation which is not generated by the constraints in the model as it is the case with the other variables. For rank one gauge theories we show how to…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
The Hamiltonian (gauge) symmetry generators of non-local (gauge) theories are presented. The construction is based on the d+1 dimensional space-time formulation of d dimensional non-local theories. The procedure is applied to U(1)…
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools…
The noncritical $4D$ $\cW_3$ string is a model of $\cW_3$ gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the $2D$ (Virasoro) string. The physical operators form a…
Variety of machine learning problems can be formulated as an optimization task for some (surrogate) loss function. Calculation of loss function can be viewed in terms of stochastic computation graphs (SCG). We use this formalism to analyze…
Opportunity cost matrices are interesting in the context of scenario reduction. We provide new algorithms, based on ideas from algebraic geometry, to efficiently compute the opportunity cost matrix using computational algebraic geometry. We…
Several examples of similarity transformations connecting two string theories with different backgrounds are reviewed. We also discuss general structure behind the similarity transformations from the point of view of the topological…
It has previously been shown that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^[Q, \psi] |\phi> where |\phi> is either a trivially BRST invariant state which only depends on the matter variables,…
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations…
In this paper, we derive new computational techniques for residue number systems (RNS) based Barrett algorithm (BA). The focus of the work is an algorithm that carries out the entire computation using only modular arithmetic without…
The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct…
The paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra…
A system of unitary transformations providing two optimal copies of an arbitrary input cubit is obtained. An algorithm based on classical Boolean algebra and allowing one to find any unitary transformation realized by the quantum CNOT…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
For the rational quantum Calogero systems of type $A_1{\oplus}A_2$, $AD_3$ and $BC_3$, we explicitly present complete sets of independent conserved charges and their nonlinear algebras. Using intertwining (or shift) operators, we include…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…