相关论文: Second quantization of the elliptic Calogero-Suthe…

It is observed that some structures recently uncovered in the study of Calogero-Sutherland models and anyons are close analogs of well-known structures of boundary conformal field theory. These examples of ``boundary conformal quantum…

In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…

The Lorentzian Hamiltonian constraint is solved for isotropic loop quantum cosmology coupled to a massless scalar field. As in the Euclidean case, the discreteness of quantum geometry removes the classical singularity from the quantum…

Matrix generalizations of the N-particle quantum-mechanical Calogero model classifying according to representations of the symmetric group $S_N$ are considered. Symmetry properties of the eigen-wave functions in the matrix Calogero models…

Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…

An alternative quantization of the gravitational Hamiltonian constraint of the $k=-1$ Friedmann-Robertson-Walker model is proposed by treating the Euclidean term and the Lorentzian term independently, mimicking the treatment of full loop…

In the foundational logical framework of homotopy-type theory we discuss a natural formalization of secondary integral transforms in stable geometric homotopy theory. We observe that this yields a process of non-perturbative cohomological…

Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result…

We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…

The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…

Characterizing quantum many-body systems is a fundamental problem across physics, chemistry, and materials science. While significant progress has been made, many existing Hamiltonian learning protocols demand digital quantum control over…

We use the collective field theory known for the Calogero-Sutherland model to study a variety of low-energy properties. These include the ground state energy in a confining potential upto the two leading orders in the particle number, the…

We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical…

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…

The U(1) Calogero Sutherland Model (CSM) with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially…

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define…

Models for topological quantum computation are based on braiding and fusing anyons (quasiparticles of fractional statistics) in (2+1)-D. The anyons that can exist in a physical theory are determined by the symmetry group of the Hamiltonian.…

We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the…

We present a cocycle model for elliptic cohomology with complex coefficients in which methods from 2-dimensional quantum field theory can be used to rigorously construct cocycles. For example, quantizing a theory of vector bundle-valued…