arXiv subjects

Satish D. Joglekar

Publications and source records attributed to Satish D. Joglekar.

At least 19 recordsLinked to original sources

arXiv2010

A self-consistent bound state model for meson

We study the 1+1 dimensional Yukawa theory, in a certain limit of its parameters g,M,m (as suggested by the study of causality in presence of bound states in this model). We study the bound state formation in the model. In the limit $g\to\infty,M\to\infty$, in a certain specific manner, we show that there are a large number of bound states of which at least the low lying states are described by the non-relativistic Schrodinger equation. We show that, in this limit, the excited bound states are unstable and deem to decay quickly (lifetime $τ\to 0 $) by emission of scalar (s) in this particular limit. The mass of the ground state is not significantly affected by higher order quantum corrections and by proper choice of parameters, involving only small changes, can be adjusted to be equal to the mass of the scalar. As a result of quantum effects, the state of the meson mixes with the lowest bound state and may be dominated by the latter .We show that in this detailed sense, a scalar meson in Yukawa model can be looked upon as a bound state of a fermion-anti fermion pair formed.

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arXiv2010

Causality in 1+1 Dimensional Yukawa Model-II

We discuss the limits g tending to large, M tending to large with g^3/M = const. of the 1 + 1 dimensional Yukawa model. We take into account conclusion of the results on bound states of the Yukawa Model in this limit (obtained in [7]). We find that model reduces to an effective nonlocal phi 3 theory in this limit. We observe causality violation in this limit. We discuss the result.

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arXiv2008

Possible Detection of Causality Violation in a Non-local Scalar Model

We consider the possibility that there may be causality violation detectable at higher energies. We take a scalar nonlocal theory containing a mass scale $Λ$ as a model example and make a preliminary study of how the causality violation can be observed. We show how to formulate an observable whose detection would signal causality violation. We study the range of energies (relative to $Λ$) and couplings to which the observable can be used.

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arXiv2008

Two Photon Exchange Contributions to Elastic e + p --> e + p Process in a Nonlocal Field Formalism

We compute the two photon exchange contributions to elastic scattering of polarized electrons from target protons. We use a nonlocal field theory formalism for this calculation. The formalism maintains gauge invariance and provides a systematic procedure for making this calculation. The results depend on one unknown parameter \bar b. We compute the two photon exchange correction to the ratio of electric to magnetic form factors extracted using the polarization transfer experiments. The correction is found to be small if \bar b ~ 1. However for larger values of \bar b>3, the correction can be quite significant. The correction to the polarization transfer results goes in the right direction to explain their difference with the ratio measured by Rosenbluth separation method. We find that the difference between the two experimental results can be explained for a wide range of values of the parameter \bar b. We also find that the corrections due to two photon exchange depend on the photon longitudinal polarization epsilon. Hence we predict an epsilon dependence of the form factor ratio extracted using the polarization transfer technique. Finally we obtain a limit on \bar b by requiring that the non-linearity in epsilon dependence of the unpolarized reduced cross section is within experimental errors.

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arXiv2007

Two Photon Exchange Contributions to Elastic ep Scattering in the Nonlocal Field Formalism

We construct a nonlocal gauge invariant Lagrangian to model the electromagnetic interaction of proton. The Lagrangian includes all allowed operators with dimension up to five. We compute the two photon exchange contribution to elastic electron-proton scattering using this effective nonlocal Lagrangian. The one loop calculation in this model includes the standard box and cross box diagram with the standard on-shell form of the hadron electromagnetic vertices. Besides this we find an extra contribution which depends on an unknown constant. We use experimentally extracted form factors for our calculation. We find that the correction to the reduced cross section is slightly nonlinear as a function of the photon longitudinal polarization $ε$. The non-linearity seen is within the experimental error bars of the Rosenbluth data. The final result completely explains the difference between the form factor ratio $G_E/G_M$ extracted by Rosenbluth separation technique at SLAC and polarization transfer technique at JLAB.

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arXiv2007

Composite Structure and Causality

We study the question of whether a composite structure of elementary particles, with a length scale $1/Λ$, can leave observable effects of non-locality and causality violation at higher energies (but $\lesssim Λ$). We formulate a model-independent approach based on Bogoliubov-Shirkov formulation of causality. We analyze the relation between the fundamental theory (of finer constituents) and the derived theory (of composite particles). We assume that the fundamental theory is causal and formulate a condition which must be fulfilled for the derived theory to be causal. We analyze the condition and exhibit possibilities which fulfil and which violate the condition. We make comments on how causality violating amplitudes can arise.

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arXiv2007

Causality in Non-Commutative Quantum Field Theories

We study causality in non-commutative quantum field theory with a space-space non-commutativity. We employ the S-operator approach of Bogoliubov-Shirkov(BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between T*-product and T-product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and one in the Yukawa theory. In particular, in the context of a non-commutative Yukawa theory, with the interaction Lagrangian $\barψ(x)\starψ(x)\starϕ(x)$, is observed to be causality violating even in case of space-space noncommutativity for which θ^{0i}=0. \

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arXiv2005

Causality Violation in Non-local QFT

We study the causality violation in the non-local quantum field theory (as formulated by Kleppe and Woodard) containing a finite mass scale $Λ$. We use $ϕ^{4}$ theory as a simple model for study. Starting from the Bogoliubov-Shirkov criterion for causality, we construct and study combinations of S-matrix elements that signal violation of causality in the one loop approximation. We find that the causality violation in the exclusive process $ϕ+ϕ\to ϕ+ϕ$ grows with energy, but the growth with energy, (for low to moderate energies) is suppressed to all orders compared to what one would expect purely from dimensional considerations. We however find that the causality violation in other processes such as $ϕ+ϕ\to ϕ+ϕ+ϕ+ϕ$ grows with energy as expected from dimensional considerations at low to moderate energies. For high enough energies comparable to the mass scale $Λ$, however, we find a rapid (exponential-like) growth in the degree of causality violation. We generalize some of the 1-loop results to all orders. We present interpretations of the results based on possible interpretations of the non-local quantum field theory models.

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arXiv2004

Relating Calculations and Renormalization in Axial and Lorentz Gauges and Gauge-independence

We study futher the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the 1-loop approximation for the wavefunction renormalization and the identity of the beta-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the 1-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave-function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the beta functions in the two gauges.

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arXiv2004

Causality Violation in Non-local Quantum Field Theory

We study the causality violation in the non-local phi ^{4}-theory (as formulated by Kleppe and Woodard) containing a finite mass scale Lambda . Starting from the Bogoliubov-Shirkov criterion for causality, we construct and study combinations of S-matrix elements that signal the violation of causality in the one loop approximation. We find that the causality violation in the exclusive process ϕ+ϕ--> ϕ+ϕgrows with energy, but the growth with energy, (for low to moderate energies) is suppressed to all orders compared to what one would expect purely from dimensional considerations. We however find that the causality violation in other processes such as ϕ+ϕ--> ϕ+ϕ+ϕ+ϕgrows with energy as expected from dimensional considerations at low to moderate energies. For high enough energies comparable to the mass scale Lambda, however, we find a rapid (exponential-like) growth in the degree of causality violation. We suggest a scenario, based on an earlier work, that will enable one to evade a large theoretical causality violation at high energies, should it be unobserved experimentally.

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arXiv2003

Additional considerations in the definition and renormalization of non-covariant gauges

In this work, we pursue further consequences of a general formalism for non-covariant gauges developed in an earlier work (hep-th/0205042). We carry out further analysis of the additional restrictions on renormalizations noted in that work. We use the example of the axial gauge A_3=0. We find that if multiplicative renormalization together with ghost-decoupling is to hold, the ``prescription-term'' (that defines a prescription) cannot be chosen arbitrarily but has to satisfy certain non-trivial conditions (over and above those implied by the validity of power counting) arising from the WT identities associated with the residual gauge invariance. We also give a restricted class of solutions to these conditions.

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arXiv2002

Some Observations on Non-covariant Gauges and the epsilon-term

We consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. From rather elementary considerations, we demonstrate the necessity of inclusion of an epsilon-term (even) in the formal treatments, without which one may reach incorrect conclusions. We show, further, that the epsilon-term can contribute to the BRST WT-identities in a nontrivial way (even as epsilon-->0). We also show that the (expectation value of the) correct epsilon-term satisfies an algebraic condition. We show by considering (a commonly used) example of a simple local quadratic epsilon -term, that they lead to additional constraints on Green's function that are not normally taken into account in the BRST formalism that ignores the epsilon-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that for a subclass of these gauges, the Minkowski path-integral could not be obtained by a Wick rotation from a Euclidean path-integral.

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arXiv2002

Interpolating Gauges,Parameter Differentiability,WT-identities and the epsilon term

Evaluation of variation of a Green's function in a gauge field theory with a gauge parameter theta involves field transformations that are (close to) singular. Recently, we had demonstrated {hep-th/0106264}some unusual results that follow from this fact for an interpolating gauge interpolating between the Feynman and the Coulomb gauge (formulated by Doust). We carry out further studies of this model. We study properties of simple loop integrals involved in an interpolating gauge. We find that the proof of continuation of a Green's function from the Feynman gauge to the Coulomb gauge via such a gauge in a gauge-invariant manner seems obstructed by the lack of differentiability of the path-integral with respect to theta (at least at discrete values for a specific Green's function considered) and/or by additional contributions to the WT-identities. We show this by the consideration of simple loop diagrams for a simple scattering process. The lack of differentiability, alternately, produces a large change in the path-integral for a small enough change in theta near some values. We find several applications of these observations in a gauge field theory. We show that the usual procedure followed in the derivation of the WT-identity that leads to the evaluation of a gauge variation of a Green's function involves steps that are not always valid in the context of such interpolating gauges. We further find new results related to the need for keeping the epsilon-term in the in the derivation of the WT-identity and and a nontrivial contribution to gauge variation from it. We also demonstrate how arguments using Wick rotation cannot rid us of these problems. This work brings out the pitfalls in the use of interpolating gauges in a clearer focus.

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arXiv2001

Interpolating gauges and the importance of a careful treatment of epsilon term

We consider the use of interpolating gauges (with a gauge function (F[A;alpha ]) in gauge theories to connect the results in a set of different gauges in the path-integral formulation. We point out that the results for physical observables are very sensitive to the epsilon term that we have to add to deal with singularities and thus cannot be left out of a discussion of gauge-independence generally. We further point out, with reasons, that the fact that we can ignore this term in the discussion of gauge independence while varying of the gauge parameter in Lorentz-type covariant gauges is an exception rather than a rule . We show that generally gauge-independence requires that the epsilon-term has to be varied with alpha. We further show that if we make a naive use of the epsilon term -i\int d^{4}x[{1/2}A^{2}-\bar{c}c]) (that is appropriate for the Feynman gauge) for general interpolating gauges with arbitrary parameter values [i.e.alpha], we cannot preserve gauge independence [except when we happen to be in the infinitesimal neighborhood of the Lorentz-type gauges]. We show with an explicit example that for such a naive use of an epsilon-term, we develop serious pathology in the path-integral as alpha is/are varied. We point out that correct way to fix the epsilon-term in a path-integral in a non-Lorentz gauge is by connecting the path-integral to the Lorentz-gauge path-integral with correct epsilon-term as has been done using the finite field-dependent BRS transformations in recent years.

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arXiv2001

The condition 0 < Z < 1 and an intrinsic mass scale in Quantum Field Theory

In this work, we suggest a view-point that leads to an intrinsic mass scale in Quantum Field Theories. This view-point is fairly independent of dynamical details of a QFT and does not rely on any particular framework to go beyond the standard Model. We use the setting of the nonlocal quantum field theories NLQFT with a finite scale parameter Lambda, which are unitary for finite Lambda. We propose that the condition 0 < Z < 1 [wherever proven] can be rigorously implemented/imposed in such theories and that it implies the existence of a mass scale Lambda that can be determined from this condition. We derive the nonlocal analogue of the above relation [which is a finite relation in NLQFT] and demonstrate that it can be arrived at only from general principles. We further propose that the nonlocal formulation should be looked as an effective field theory that incorporates the effect of dynamics beyond an energy scale and which breaks at the intrinsic scale Lambda so obtained. Beyond this scale it should be replaced by another [perhaps, a more fundamental] theory. We provide a heuristic justification for this view-point.

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arXiv2000

Green's Functions in Axial and Lorentz-type Gauges and Application to The Axial Pole Prescription and The Wilson Loop

We summarize the work done in connecting Green's functions in a different classes of gauges and its applications to the problems in the axial gauges.The procedure adopted uses finite field-dependent BRS [FFBRS] transformations to connect axial and the Lorentz type gauges.These transformations preserve the vacuum expectation of gauge-invariant observables explicitly. We discuss the applications of these ideas to the axial gauge pole problem and to the preservation of the Wilson loop and the thermal Wilson loop.

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arXiv2000

Wilson Loop and the Treatment of Axial Gauge Poles

We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that as under the FFBRS transformation the vacuum expectation value of a gauge invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Further, we give an argument for {\it direct} verification of the invariance of Wilson loop to O(g^4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wilson loop to O(g^2).

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arXiv2000

Connecting Green's Functions in an Arbitrary Pair of Gauges and an Application to Planar Gauges

We establish a finite field-dependent BRS transformation that connects the Yang-Mills path-integrals with Faddeev-Popov effective actions for an arbitrary pair of gauges F and F'. We establish a result that relates an arbitrary Green's function [either a primary one or one that of an operator] in an arbitrary gauge F' to those in gauge F that are compatible to the ones in gauge F by its construction [in that the construction preserves expectation values of gauge-invariant observables]. We establish parallel results also for the planar gauge-Lorentz gauge connection.

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