arXiv subjects

Raghunath Ratabole

Publications and source records attributed to Raghunath Ratabole.

15 recordsLinked to original sources

arXiv2026

Hamiltonian formulation of the $1+1$-dimensional $ϕ^4$ theory in a momentum-space Daubechies wavelet basis

We apply the wavelet formalism of quantum field theory to investigate nonperturbative dynamics within the Hamiltonian framework. In particular, we employ Daubechies wavelets in momentum space, whose basis functions are labeled by resolution and translation indices, providing a natural nonperturbative truncation of both infrared and ultraviolet truncation of quantum field theories. As an application, we compute the energy spectra of a free scalar field theory and the interacting $1+1$-dimensional $ϕ^4$ theory. This approach successfully reproduces the well-known strong-coupling phase transition in the $m^2 > 0$ regime. We find that the extracted critical coupling systematically converges toward its established value as the momentum resolution is increased, demonstrating the effectiveness of the wavelet-based Hamiltonian formulation for nonperturbative field-theoretic calculations.

hep-th↗

arXiv2025

Hamiltonian Flow Equations in Daubechies Wavelet Basis

We study the low energy dynamics of a system of two coupled real scalar fields in 1+1 dimensions using the flow equation approach of Similarity Renormalization Group (SRG) in a wavelet basis. This paper presents an extension of the work by Michlin and Polyzou \cite{PhysRevD.95.094501} at one resolution higher. We also present the analysis of a model of two scalar fields coupled through a generally quadratic interaction in $1+1$ dimensions using wavelet-based flow equations. We demonstrate that the specifically chosen generator flows the Hamiltonian into a block diagonal form with each diagonal block being associated with a fixed resolution. The wavelet basis is known to transform the scalar field theory into a model of coupled localized oscillators, each of which is labelled by location and resolution indices. The chosen interaction represents the coupling between two types of oscillators at the same location and resolution index. There is no coupling between oscillators across locations and resolutions. We show that wavelet-based flow equations carry out scale separation while maintaining the interactions between the two scalar fields at each resolution. The effective Hamiltonian associated with the coarsest resolution is shown to correctly reproduce the normal mode frequencies of the model.

hep-th↗

arXiv2023

Renormalization in Wavelet basis

Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based methods. We demonstrate the non-perturbative approach of regularization, renormalization, and the emergence of flowing coupling constant within the context of these methods. This is tested on a model of the particle in an attractive Dirac delta function potential in two spatial dimensions, which is known to demonstrate quintessential features found in a typical relativistic quantum field theory.

hep-th↗

arXiv2020

Quantum Mechanics in Wavelet Basis

We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis function as a quantum fluctuation of a specific resolution at a particular location. The Hamiltonian matrix constructed in this basis describes couplings between different length scales and thus allows for intuitive volume and resolution truncation. In quantum mechanical problems with a natural length scale, one can get approximate solution of the problem through simple matrix diagonalization. We illustrate this approach using the example of the standard quantum mechanical simple harmonic oscillator.

quant-ph↗

arXiv2013

Comment on Phys. Rev. Lett. 109, 152005 (2012)

The identifications of transverse boost and rotation operators in light front theory done in Phys. Rev. Lett. {109}, 152005 (2012) is incorrect. The simple parton interpretation claimed is, in fact, for the transverse boost operator. Manifestation of Lorentz symmetry as claimed in the context of their calculation involving transverse Pauli-Lubanski polarization vector is unsupported.

hep-ph↗

arXiv2007

Instability in scalar channel of fermion-antifermion scattering amplitude in massless QED_3 and anomalous dimensions of composite operators

Instability in the scalar channel of the fermion-antifermion scattering amplitude in massless QED_3 for number of flavours less than the critical value 128/3π^2 is demonstrated. The anomalous dimensions of gauge-invariant composite operators are determined to O(1/N). Exponentiation of the O(1/N) infrared logarithm is explicitly demonstrated by evaluating the contribution of the ladder diagrams.

hep-th↗

arXiv2006

Gauge dependence of the infrared behaviour of massless QED_3

Using the Zumino identities it is shown that in a class of non-local gauges, massless QED_3 has an infrared behaviour of a conformal field theory with a continuously varying anomalous dimension of the fermion. In the usual Lorentz gauge, the fermion propagator falls off exponentially for a large separation, but this apparent fermion mass is a gauge artifact.

hep-th↗

arXiv2005

Large-N QCD at strong transverse lattice gauge coupling

We had previously obtained an integral equation for mesons in transverse lattice QCD, in the limit of large number of colours and strong transverse lattice gauge coupling [1]. This equation is a generalisation of the 't Hooft equation [2], by inclusion of the spin degrees of freedom. We analyse this equation to extract spectral properties and light-front wavefunctions of mesons. We also extend the method to study baryon properties in the same limit.

hep-lat↗

arXiv2005

Gauge-invariant dressed fermion propagator in massless QED_3

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED_3 is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement.

hep-th↗

arXiv2005

A Transverse Lattice QCD Model for Mesons

This thesis describes work done by me during my tenure as a Ph.D. student at the Centre for High Energy Physics, Indian Institute of Science, Bangalore. Chapter 1 is a brief introduction to QCD. In Chapter 2, we formulate QCD in the large-$N_{c}$ and strong transverse coupling limits, and then exactly integrate out all the gauge degrees of freedom to obtain the generating functional for quark-antiquark bilinears. We study the chiral properties of our limiting theory in Chapter 3, for naive as well as Wilson fermions, and obtain a recursive relation for the chiral condensate. In Chapter 4, we obtain the homogeneous integral equation satisfied by the meson states of our theory. Comparison of this equation with the corresponding one for the 't~Hooft model allows us to infer many physical meson properties. Our results are consistent with phenomenological expectations, and this is the first time that such results have been obtained from $(3+1)$-dim QCD, with only quark and gluon degrees of freedom and no ad hoc model assumptions. Extraction of precise values requires numerical solution of the integral equation; we have not yet carried that out and we describe our outlook for further investigations at the end of Chapter 4. Three appendices supplement our analysis. Our notation and conventions are listed in Appendix A. The known results for mesons in the 't~Hooft model and in strong coupling lattice QCD are rederived, in Appendix B and in Appendix C respectively, using the same methodology as followed in the thesis. That allows convenient comparison, as well as demonstrates the advantage of our approach over these two well-studied approximations to QCD.

hep-lat↗

arXiv2005

Infrared behaviour of massless QED in space-time dimensions 2 < d < 4

We show that the logarithmic infrared divergences in electron self-energy and vertex function of massless QED in 2+1 dimensions can be removed at all orders of 1/N by an appropriate choice of a non-local gauge. Thus the infrared behaviour given by the leading order in 1/N is not modified by higher order corrections. Our analysis gives a computational scheme for the Amati-Testa model, resulting in a non-trivial conformal invariant field theory for all space-time dimensions 2 < d < 4.

hep-th↗

arXiv2003

A Transverse Lattice QCD Model for Mesons

QCD is analysed with two light-front continuum dimensions and two transverse lattice dimensions. In the limit of large number of colours and strong transverse gauge coupling, the contributions of light-front and transverse directions factorise in the dynamics, and the theory can be analytically solved in a closed form. An integral equation is obtained, describing the properties of mesons, which generalises the 't Hooft equation by including spin degrees of freedom. The meson spectrum, light-front wavefunctions and form factors can be obtained by solving this equation numerically. These results would be a good starting point to model QCD observables which only weakly depend on transverse directions, e.g. deep inelastic scattering structure functions.

hep-lat↗

arXiv2000

Transverse Spin in QCD: Radiative Corrections

In this paper we address various issues connected with transverse spin in light front QCD. The transverse spin operators, in $A^+ = 0$ gauge, expressed in terms of the dynamical variables are explicitly interaction dependent unlike the helicity operator which is interaction independent in the topologically trivial sector of light-front QCD. Although it cannot be separated into an orbital and a spin part, we have shown that there exists an interesting decomposition of the transverse spin operator. We discuss the physical relevance of such a decomposition. We perform a one loop renormalization of the full transverse spin operator in light-front Hamiltonian perturbation theory for a dressed quark state. We explicitly show that all the terms dependent on the center of mass momenta get canceled in the matrix element. The entire non-vanishing contribution comes from the fermion intrinsic -like part of the transverse spin operator as a result of cancellation between the gluonic intrinsic-like and the orbital-like part of the transverse spin operator. We compare and contrast the calculations of transverse spin and helicity of a dressed quark in perturbation theory.

hep-th↗

arXiv2000

Transverse Spin in QCD. I. Canonical Structure

In this work we initiate a systematic investigation of the spin of a composite system in an arbitrary reference frame in QCD. After a brief review of the difficulties one encounters in equal-time quantization, we turn to light-front quantization. We show that, in spite of the complexities, light-front field theory offers a unique opportunity to address the issue of relativistic spin operators in an arbitrary reference frame since boost is kinematical in this formulation. Utilizing this symmetry, we show how to introduce transverse spin operators for massless particles in an arbitrary reference frame in analogy with those for massive particles. Starting from the manifestly gauge invariant, symmetric energy momentum tensor in QCD, we derive expressions for the interaction dependent transverse spin operators ${\cal J}^i$ ($i=1,2$) which are responsible for the helicity flip of the nucleon in light-front quantization. In order to construct ${\cal J}^i$, first we derive expressions for the transverse rotation operators $F^i$. In the gauge $A^+=0$, we eliminate the constrained variables. In the completely gauge fixed sector, in terms of the dynamical variables, we show that one can decompose ${\cal J}^i= {\cal J}^i_I + {\cal J}^i_{II} + {\cal J}^i_{III}$ where only ${\cal J}^i_{I}$ has explicit coordinate ($x^-, x^i$) dependence in its integrand. The operators ${\cal J}^i_{II}$ and ${\cal J}^i_{III}$ arise from the fermionic and bosonic parts respectively of the gauge invariant energy momentum tensor. We discuss the implications of our results.

hep-th↗

arXiv2000

Transverse Spin in QCD and Transverse Polarized Deep Inelastic Scattering

We address the long standing problem of the construction of relativistic spin operators for a composite system in QCD. Exploiting the kinematical boost symmetry in light front theory, we show that transverse spin operators for massless particles can be introduced in an arbitrary reference frame, in analogy with those for massive particles. In light front QCD, the complete set of transverse spin operators are identified for the first time, which are responsible for the helicity flip of the nucleon. We establish the direct connection between transverse spin in light front QCD and transverse polarized deep inelastic scattering. We discuss the theoretical and phenomenological implications of our results.

hep-ph↗