Related papers: Perturbative BV-BFV formalism with homotopic renor…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
We introduce a formulation of combined systems in orthodox non-relativistic quantum mechanics, mathematically equivalent to the usual one. For context and larger issues, see http://euclid.unh.edu/~jjohnson/axiomatics.html and…
The purpose of this Chapter is to give a general introduction and status review on the perturbative approach to quantum gravity (QG). This text is a modified version of the corresponding chapters of Part II of the recent textbook on quantum…
We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As…
Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We…
We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related…
In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type…
We apply the gaussian variational method (GVM) to study the equilibrium statistical mechanics of the two related systems: (i) classical elastic manifolds, such as flux lattices, in presence of columnar disorder correlated along the $\tau$…
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations.…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
We show that the Kaehler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kaehler manifold. By introducing an isometry we explicitly construct the fermionic…
The biorthogonal formalism extends conventional quantum mechanics to the non-Hermitian realm. It has, however, been pointed out that the biorthogonal inner product changes with the scaling of the eigenvectors, an ambiguity whose physical…
Any regular quantum mechanical system may be cast into an abelian gauge theory by simply reformulating it as a reparametrization invariant theory. We present a detailed study of the BRST quantization of such reparametrization invariant…
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of…
This note gives an introduction to Lagrangian field theories in the presence of boundaries. After an overview of the classical aspects, the cohomological formalisms to resolve singularities in the bulk and in the boundary theories (the BV…
The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the…
In this work we present a re-evaluation of the concept of time in non-relativistic quantum theory. We suggest a formalism in which time is changed into the status of an operator, and where expectation values of observables and the state of…