Related papers: Nonrelativistic Quantum Hamiltonian for Lorentz Vi…
After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum…
The Green function of the quark-antiquark system in the confining background field is analysed using the Feynman-Schwinger formalism. The Hamiltonian for the case of massive spinning quarks is obtained in the form containing essentially…
While fundamental physically realistic Hamiltonians should be invariant under time reversal, time asymmetric Hamiltonians can occur as mathematical possibilities or effective Hamiltonians. Here, we study conditions under which…
The existing derivations of a heavy quark effective theory (HQET) are analyzed beyond the next-to-leading order in $1/m$. With one exception they are found to be incorrect. The problem is a wrong normalization of the heavy quark field in…
We construct a solution to the equation of motion of Hamiltonian lattice QCD in the strong coupling limit using Wilson fermions which exactly diagonalizes the Hamiltonian to second order in the field operators. This solution obeys the free…
We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell…
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an…
Theories with an infinite number of derivatives are described by non-local Lagrangians for which the standard Hamiltonian formalism cannot be applied. Hamiltonians of special types of non-local theories can be constructed by means of the…
The Hamiltonian and Lagrangian formalisms of Qunatum Field Theory (QFT) are equivalent. But while Lorentz invariance can be clearly seen in the Lagrangian formalism, it is not so explicit in the Hamiltonian one. This is because time is…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional…
In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical value $\gamma^*$ may exist such that, when $\gamma=\gamma^*$, the leading irrelevant operator decouples from the Hamiltonian and the leading nonscaling contribution…
We describe non-relativistic fermions on the lattice (Hubbard model) in the canonical formulation using transfer matrices in fixed fermion number sectors such that the partition function becomes fully factorized in time. By analytically…
We consider the question of existence of Hamiltonians for autonomous non-holonomic mechanical systems in this paper. The approach is elementary in the sense that the existence of a Hamiltonian for a given non-holonomic system is considered…
In this talk I review the calculation of the third order corrections to the heavy quarkonium spectrum in the nonrelativistic effective theory framework and its application to the phenomenology of top quark threshold production.
We present a detailed Hamiltonian treatment of an inhomogeneous fermionic perturbation propagating on a closed FLRW spacetime quantized via LQC. Expanding the fermion in spinor harmonics on spatial 3-sphere and truncating at quadratic…
Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method…
We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the…
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
The quantum Lifshitz model provides an effective description of a quantum critical point. It has been shown that even though non--Lorentz invariant, the action admits a natural supersymmetrization. In this note we introduce a perturbative…