arXiv subjects

Lubomir Martinovic

Publications and source records attributed to Lubomir Martinovic.

10 recordsLinked to original sources

arXiv2021

Vacuum loops in light-front field theory

We demonstrate that vacuum diagrams in the genuine light front (LF) field theory are non-zero, in spite of simple kinematical counter-arguments (positivity and conservation of the LF momentum $p^+$, absence of Fourier zero mode). Using the light-front Hamiltonian (time-ordered) perturbation theory, the vacuum amplitudes in self-interacting scalar $λϕ^3$ and $λϕ^4$ models are obtained as $p=0$ limit of the associated self-energy diagrams, where $p$ is the external momentum. They behave as $Cλ^2μ^{-2}$ in D=2, with $μ$ being the scalar-field mass, or diverge in D=4, in agreement with the usual "equal-time" form of field theory, and with the same value of the constant $C$. The simplest case of the vacuum bubble with two internal lines is analyzed in detail, displaying the subtle role of the small $k^+$ region and its connection to the $p=0$ limit. However, the vacuum bubbles in the genuine light-front field theory are non-vanishing not due to the Fourier mode carrying LF momentum $k^+=0$ (as is the case in the LF evaluation of the covariant Feynman diagrams), in full accord with the observation that the LF perturbation theory formula breaks down in the exact zero-mode case. This is made explicit using the DLCQ method - the discretized (finite-volume) version of the theory, where the light-front zero modes are manifestly absent, but the vacuum amplitudes still converge to their continuum-theory values with the increasing "harmonic resolution" K.

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arXiv2012

New operator solution of the Schwinger model in a covariant gauge and axial anomaly

Massless QED(1+1) - the Schwinger model - is studied in a covariant gauge. The main new ingredient is an operator solution of the Dirac equation expressed directly in terms of the fields present in the Lagrangian. This allows us to study in detail the residual symmetry of the covariant gauge. For comparison, we analyze first an analogous solution in the Thirring-Wess model and its implication for the axial anomaly arising from the necessity to correctly define products of fermion operators via point-splitting. In the Schwinger model, one has to define the currents in a gauge invariant (GI) way. Certain problems with their usual derivation are identified that obscure the origin of the massive vector boson. We show how to define the truly GI interacting currents, reformulate the theory in a finite volume and clarify role of the gauge zero mode in the axial anomaly and in the Schwinger mechanism. A transformation to the Coulomb gauge representation is suggested along with ideas about how to correctly obtain other properties of the model.

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arXiv2011

Exactly solvable models and spontaneous symmetry breaking

We study a few two-dimensional models with massive and massless fermions in the hamiltonian framework and in both conventional and light-front forms of field theory. The new ingredient is a modification of the canonical procedure by taking into account solutions of the operator field equations. After summarizing the main results for the derivative-coupling and the Thirring models, we briefly compare conventional and light-front versions of the Federbush model including the massive current bosonization and a Bogoliubov transformation to diagonalize the Hamiltonian. Then we sketch an extension of our hamiltonian approach to the two-dimensional Nambu--Jona-Lasinio model and the Thirring--Wess models. Finally, we discuss the Schwinger model in a covariant gauge. In particular, we point out that the solution due to Lowenstein and Swieca implies the physical vacuum in terms of a coherent state of massive scalar field and suggest a new formulation of the model's vacuum degeneracy.

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arXiv2011

Hamiltonian formulation of exactly solvable models and their physical vacuum states

We clarify a few conceptual problems of quantum field theory on the level of exactly solvable models with fermions. The ultimate goal of our study is to gain a deeper understanding of differences between the usual ("spacelike") and light-front forms of relativistic dynamics. We show that by incorporating solutions of the operator field equations to the canonical formalism the spacelike and light front Hamiltonians of the derivative-coupling model acquire an equivalent structure. The same is true for the massive solvable theory, the Federbush model. In the conventional approach, the physical predictions in the two schemes disagree. Moreover, the derivative-coupling model is found to be almost identical to a free theory, in contrast to the conventional canonical treatment. Physical vacuum state of the Thirring model is then obtained by a Bogoliubov transformation as a coherent state quadratic in composite boson operators. To perform the same task in the Federbush model, we derive a massive version of Klaiber's bosonization and show that its light-front form is much simpler.

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arXiv2010

Hamiltonians and physical vacua of exactly solvable models

Correct quantum Hamiltonians of a few exactly solvable models in two space-time dimensions are derived by taking into account operator solutions of the field equations. While two versions of the model with derivative coupling are found to be equivalent in many respects to a free theory, physical vacua of the massless Thirring and Federbush models are obtained by means of a Bogoliubov transformation in the form of a coherent state quadratic in composite boson operators. Contrary to the conventional treatment, the Federbush model is shown to have the same interacting structure in both space-like and light-front formulations.

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arXiv2006

Higgs mechanism in a light front formulation

We give a simple derivation of the Higgs mechanism in an abelian light front field theory. It is based on a finite volume quantization with antiperiodic scalar fields and a periodic gauge field. An infinite set of degenerate vacua in the form of coherent states of the scalar field that minimize the light front energy, is constructed. The corresponding effective Hamiltonian descibes a massive vector field whose third component is generated by the would-be Goldstone boson. This mechanism, understood here quantum mechanically in the form analogous to the space-like quantization, is derived without gauge fixing as well as in the unitary and the light cone gauge.

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arXiv2005

Ab initio results for the broken phase of scalar light front field theory

We present nonperturbative light-front energy eigenstates in the broken phase of a two dimensional $\fracλ{4!}ϕ^4$ quantum field theory using Discrete Light Cone Quantization and extrapolate the results to the continuum limit. We establish degeneracy in the even and odd particle sectors and extract the masses of the lowest two states and the vacuum energy density for $λ=0.5$ and 1.0. We present two novel results: the Fourier transform of the form factor of the lowest excitation as well as the number density of elementary constituents of that state. A coherent state with kink - antikink structure is revealed.

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arXiv2004

Analytic solution of the microcausality problem in Discretized Light Cone Quantization

It is shown that that violation of causality in two-dimensional light-front field theories quantized in a finite ``volume'' $L$ with periodic or antiperiodic boundary conditions is marginal and vanishes smoothly in the continuum limit. For this purpose, we derive an exact integral representation for the complete infinite series expansion of the two-point functions of a free massive scalar and fermi field for an arbitrary finite value of $L$ and show that in the $L \to \infty$ limit we retrieve the correct continuum results.

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arXiv2003

Kinks in Discrete Light Cone Quantization

We investigate non-trivial topological structures in Discrete Light Cone Quantization (DLCQ) through the example of the broken symmetry phase of the two dimensional $ϕ^4$ theory using anti periodic boundary condition (APBC). We present evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extract the vacuum energy and kink mass and compare with classical and semi - classical results. We compare the DLCQ results for the number density of bosons in the kink state and the Fourier transform of the form factor of the kink with corresponding observables in the coherent variational kink state.

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arXiv1998

Theta-Vacuum of the Bosonized Massive Light-Front Schwinger Model

The massive Schwinger model in bosonic representation is quantized on the light front using the Dirac--Bergmann method. The non-perturbative theta- vacuum in terms of coherent states of the gauge-field zero mode is derived and found to coincide with the massless case. On the other hand, the mass term becomes highly non-linear due to the constrained zero mode of the scalar field. A non-trivial mixing between the normal-mode and zero-mode sectors of the model is crucial for the correct calculation of the theta-dependence of the leading order mass correction to the chiral condensate.

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