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In this work, we study the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, we formulate the…
We reproduce and review some of the main results of three of our earlier papers, utilizing in doing so a considerably more transparent formalism than originally utilized. The most fundamental result to which we pay especial attention in…
In this note we derive Dyson-Schwinger hierarchy of the equations for the correlators of reggeized gluon fields in the framework of Lipatov's high energy QCD effective action formalism, \cite{LipatovEff,Our1,Our2,Our3,Our4}. The explicit…
We present a method to determine the model Hamiltonians to treat rare-earth multiplets in solids from the results of the quasiparticle self-consistent \textit{GW} (QSGW) method. We apply the method to trivalent Eu compounds EuCl$_3$, EuN,…
Motivated by recent works on Hamiltonian circle actions satisfying certain minimal conditions, in this paper, we consider Hamiltonian circle actions satisfying an almost minimal condition. More precisely, we consider a compact symplectic…
The quantization of a massive spin $1/2$ field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-hermitian quantum field theory by the redefinition of the field dual and…
A conformal field theory representing a four-dimensional classical solution of heterotic string theory is presented. The low-energy limit of this solution has U(1) electric and magnetic charges, and also nontrivial axion and dilaton fields.…
Exact conformal field theories (CFTs) are obtained by using the approach of Poisson-Lie (PL) T-duality in the presence of spectators. We explicitly construct some non-Abelian T-dual $\sigma$-models (here as the PL T-duality on a…
We construct a finite model of 't Hooft's shock wave commutation relations from the ansatz\cite{Carlip}\cite{Solodukhin}\cite{BZ} that the quantum degrees of freedom in a causal diamond in a solution of Einstein's Equations are those of a…
A fundamental axiom of quantum mechanics requires the Hamiltonians to be Hermitian which guarantees real eigen-energies and probability conservation. However, a class of non-Hermitian Hamiltonians with Parity-Time ($\mathcal{PT}$) symmetry…
We present a new theorem concerning a sufficient condition for a symmetric operator acting in a complex Hilbert space to be essentially self-adjoint. By applying the theorem, we prove that the Dirac Maxwell Hamiltonian, which describes a…
Over the past few years, Hamiltonian effective field theory has been successfully applied to studies of nucleon and hyperon excited states. By discretizing the Hamiltonian in a finite volume, one can obtain the energy spectrum and compare…
Full $d$-manifold DMFT with numerically exact solvers has remained computationally prohibitive for spin-orbit materials due their scaling and severe sign problem, forcing the community to rely on simplified one- and three-band models that…
Our main result is the complete set of explicit conditions necessary and sufficient for isochronicity of a Hamiltonian system with one degree of freedom. The conditions are presented in terms of Taylor coefficients of the Hamiltonian…
We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground…
It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan-Wigner transformation is used to map physical spin…
In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. Inspired to the recent paper \cite{gb2}, see also \cite{ch} and \cite{pacini}, we study Lagrangian orbits of…
We reexamine in detail the problem of fermions interacting with a non-Abelian random vector potential. Without resorting to the replica or supersymmetry approaches, we show that in the limit of infinite disorder strength the theory…