Related papers: Quantum Operations in Algebraic QFT
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
In the current paper the properties of a quantum field theory based on certain sets of Lorentz-violating coefficients in the nonminimal fermion sector of the Standard-Model Extension are analyzed. In particular, three families of…
For a given conformal field theory (CFT), one can deform it via the addition of a marginal operator to the spectrum. In two dimensions, when the added operator has conformal weights $h=\bar{h}=1$, conformal symmetry is not broken and the…
We use the embedding formalism to study correlation functions of a d-dimensional Euclidean CFT in the presence of a $q$ co-dimensional defect. The defect breaks the global conformal group $SO(d+1,1)$ into $SO(d-q+1,1) \times SO(q)$. We…
This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a…
We study four-dimensional conformal field theories (CFTs) with an abelian $U(1)$ global symmetry using the conformal bootstrap approach. We obtain numerical bounds on the scaling dimensions of low-lying operators, the stress-tensor central…
Inspired by classical ("actual") Quantum Theory over $\mathbb{C}$ and Modal Quantum Theory (MQT), which is a model of Quantum Theory over certain finite fields, we introduce General Quantum Theory as a Quantum Theory -- in the K{\o}benhavn…
Conformal field theories (CFTs) with $U(m)\times U(n)$ global symmetry in $d=3$ dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs…
Inclusions and extensions lie at the heart of physics and mathematics. The most relevant kind of inclusion in quantum systems is that of a von Neumann subalgebra, which is the focus of this work. We propose an object intrinsic to a given…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…
We establish an operator algebra generalization of Watrous' theorem \cite{watrous2009} on mixing unital quantum channels (completely positive trace-preserving maps) with the completely depolarizing channel, wherein the more general objects…
We explore the formulation of non-rational 2D quantum gravity in terms of a chiral CFT on a Riemann surface associated with the target space. The CFT in question is constructed as the collective theory for a matrix chain, which is dual to a…
We give a general construction relating Narain rational conformal field theories (RCFTs) and associated 3d Chern-Simons (CS) theories to quantum stabilizer codes. Starting from an abelian CS theory with a fusion group consisting of $n$…
Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to…
In this paper, we pursue the discussion of the connections between rational conformal field theories (CFT) and graphs. We generalize our recent work on the relations of operator product algebra (OPA) structure constants of $sl(2)\,$…
We study the Schr\"odinger equation in quantum field theory (QFT) in its functional formulation. In this approach quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain…
In this work, we revisit the operator-state correspondence in the Majorana conformal field theory (CFT) with emphasis on its semion representation. Whereas the semion representation (or $Z_{2}$ extension of the chiral Ising CFT) gives a…
We introduce regular charts as physical reference frames in spacetime, and we show that general spacetimes can always be fully captured by regular charts. Effective quantum field theories (QFTs) can be conveniently defined in regular…
One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems…