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We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat…
Geminal wavefunctions have been employed to model strongly-correlated electrons. These wavefunctions represent products of weakly-correlated pairs of electrons and reasonable approximations are computable with polynomial cost. In…
We show that certain space of vector valued harmonic weak Maass forms of half integral weight is isomorphic to a space of scalar valued ones whose Fourier coefficients are supported on suitable progressions. This kind of result for…
An estimate has been made of the masses of heavy hadrons in nonrelativistic quark model, which includes spin and flavor-dependent hyperfine splitting for two quarks. The effect of variation of the wavefunction value at origin and the strong…
We study magnetized orbifold models. We assume the localized Fayet-Iliopoulos terms and the corresponding gauge background. Such terms lead to strong localization of zero-mode wavefunc- tions. In this setup, we compute quark mass matrices.
We develop geometric methods to study the generating weights of free modules of vector valued modular forms of half-integral weight, taking values in a complex representation of the metaplectic group. We then compute the generating weights…
We introduce a topological gauge vector potential which influences spin wave excitations over arbitrary non-uniform, slowly moving magnetization distribution. The time-component of the gauge potential plays a principal role in magnetization…
In our first article in this series ("Modular Invariant of Quantum Tori I: Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of quantum tori was defined. In this paper, we consider the case of the quantum torus…
We present results from numerical simulations of the interaction of internal gravity waves (IGW) with magnetic fields in the radiative interior of the Sun. In this second paper, the waves are forced self-consistently by an overlying…
In this paper, we study the gravitational wave polarization modes for some particular $f(R)$ models using Newman-Penrose formalism. We find two extra scalar modes of gravitational wave (longitudinal and transversal modes) in addition to two…
After an introduction emphasizing the importance of the gravitomag- netic effect in general relativity, with a resume of some space-based appli- cations, we discuss the so-called magnetic components of gravitational waves (GWs), which have…
A theory of magnetophonon resonance in quantum wells in a magnetic field tilted to the perpendicular to 2DEG is developed. The resonance is due to the resonant interaction of 2D conduction electrons with the longitudinal optic phonons. The…
We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling…
We report the exact wave functions for the eigen state of a disk-shaped two dimensional topological insulator. The property of the edge state whose energy lies inside the bulk gap is studied. It is found that the edge state energy is…
Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the…
In this study, we examine the modular transformations of the (root-)$\text{T}\overline{\text{T}}$ deformed torus partition function of a two-dimensional CFT (with a gravitational anomaly) from the holographic perspective by computing the…
We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place.
It is well known that massless Goldstone bosons have not yet been observed. In the Goldstone boson model, after the spontaneous symmetry breaking under $U(1)$, two coupled nonlinear equations are obtained for which we present the exact…
It is shown that the quantized Teichm"uller spaces have factorization properties like those required in the definition of a modular functor.
It is shown that both the electric and magnetic dipole moment vectors of hydrogen atom in the excited states with wave function $$ u_n^{(\pm)} = {1\over\sqrt 2} [R_{n,n-1}(r) Y_{n-1,\pm (n-2)}(\theta\phi) \pm R_{n,n-2}(r) Y_{n-2,\pm…