Related papers: Automating Equational Proofs in Dirac Notation
An important aspect of artificial intelligence (AI) is the ability to reason in a step-by-step "algorithmic" manner that can be inspected and verified for its correctness. This is especially important in the domain of question answering…
Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…
Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…
The \emph{Entscheidungsproblem}, or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order \emph{theories}, i.e.,…
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta respectively is performed. The ``first reduce and then quantize'' and the ``first quantize…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
Second quantization has been widely used in quantum mechanics and quantum chemistry, which is trivial and error-prone for researchers. Fortunately it is a good candidate for automatic evaluation with its simple, trivial and intrinsic…
We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among other things. At the quantum level, we…
The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets…
The main goal of this work is to study the Dirac oscillator as a quantum field using the canonical formalism of quantum field theory and to develop the canonical quantization procedure for this system in $(1+1)$ and $(3+1)$ dimensions. This…
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…
\emph{Semi-Automated Text Classification} (SATC) may be defined as the task of ranking a set $\mathcal{D}$ of automatically labelled textual documents in such a way that, if a human annotator validates (i.e., inspects and corrects where…
Functional validation is necessary to detect any errors during quantum computation. There are promising avenues to debug quantum circuits using runtime assertions. However, the existing approaches rely on the expertise of the verification…
We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation and discuss gauge freedom and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
The paper proposes an algorithm for regularization of the self-energy expressions for a Dirac particle that meets the relativistic and gauge invariance requirements.
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…