In this paper we consider the Hamiltonian of quantum electrodynamics, which describes the system of Dirac fields coupled to quantized radiation fields. We impose ultraviolet cutoffs on the Dirac field and the radiation field, and introduce spatial cutoffs to define the Hamiltonian as a self-adjoint operator on a boson-fermion Fock space. Taking a scaling limit of the Hamiltonian, we derive the ...

In this paper we solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics and establish that this nontrivial special class of Hamiltonian operators is closely connected with the associativity equations of twodimensional topological quantum field theories and the theory of Frobenius manifolds. It is shown that the Hamiltonian operators of this cla...

in this paper energy bands and berry curvature of graphene was studied. desired hamiltonian regarding the next-nearest neighbors obtained by tight binding model. by using the second quantization approach, the transformation matrix is calculated and the hamiltonian of system is diagonalized. with this hamiltonian, the band structure and wave function can be calculated. by using calculated wave f...

In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is straightforward. Imposition of the Gauss constraint can be done on the kinematical Hilbert space to select subspace of gauge invariant states. We carry out the qua...

We consider general systems consisting of n components, like ensembles of atoms or molecules, together with forces centrally binding to components or due to interactions, whose quantities are known. From these quantities we derive an energy function that represents the energy of the whole ensemble without making use of the Hamiltonian operator. We show that in this way we can find the energy fu...

Our rigorous path integral is extended to quantum evolution on metricaffine manifolds. 1 Path Integrals on Euclidean Spaces. Consider the evolution operator U [ψ(t, q)] = ψ(t, q), t ≥ t, of the quantum evolution equation on L(R): h̄ i ∂ψ(t, q)/∂t+ f(t, q, h̄ i ∂/∂q)ψ(t, q) = 0. Here the operator f(t, q, h̄ i ∂/∂q) is the standard quantization of a classical timedependent quasi-Hamiltonian f(t, q, ...

We consider a two-parameter nonhermitean quantum-mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other PT symmetric models which require special i...

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear mo...

error group, 54Addelman and Kempthorne, 60adiabatic, 171adiabatic quantum computing, 171adjacency matrix, 94adjoint action, 76, 90amplification, 149annihilation operator, 134annihilator, 49, 50minimal, 50Arthur-Merlin games, 147average Hamiltonian, 44average Hamiltonian theory, 44 Bloch sphere, 33Bloch vector, 33BPP, 31BQP, 30 Carathéo...

We derive a model Hamiltonian whose ground state expectation value of any two-body operator coincides with that obtained with the Jastrow correlated wave function of the many-body Fermi system. Using this Hamiltonian we show that the variational principle can be extended to treat systems with dynamical mesons, even if in this case the concept of wave function looses its meaning.