Related papers: Numerical Object Oriented Quantum Field Theory Cal…
Explicit realizations of quantum field theory (QFT) are admitted by a revision to the Wightman axioms for the vacuum expectation values (VEV) of fields. The technical development of QFT is expanded beyond positive functionals on *-algebras…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states…
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
These are lecture notes of the QFT-I course I gave in an online mode at Chennai Mathematical Institute. The course focussed on the free relativistic quantum fields, their interactions in the perturbative scattering framework, standard…
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
TBTK is a software development kit for quantum mechanical calculations and is designed to enable the development of applications that investigate problems formulated on second-quantized form. It also enables method developers to create…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
Quantum Implicit Neural Representations (QINRs) include components for learning and execution on gate-based quantum computers. While QINRs recently emerged as a promising new paradigm, many challenges concerning their architecture and…
Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers…
QFT vector models are a newly developed approach to quantum gravity, which are based on induced gravity in discrete spacetimes. Here we review some basic definitions and properties of these models and point out directions for future…
We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions whose Lorentz-invariant coefficient functions…
The space, on which quantum field operators are given, is constructed in any theory, in which the usual product between test functions is substituted by the $\star$-product (the Moyal-type product). The important example of such a theory is…
We compare different approaches to quantum ontology. In particular, we discuss an interpretation of quantum mechanics that we call objective quantum field theory (OQFT), which involves retrocausal fields. Here, objective implies the…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
This paper provides explicit and detailed quantum field theory (QFT) computations of polarizations correlations of emerging particles in several processes in QED, Electroweak Theory, and even in particle productions from strings, and hence…