Scalar Theories and Symmetry Breaking in the Light-Front Coupled-Cluster Method

We extend the light-front coupled-cluster (LFCC) method to include zero modes explicitly, in order to be able to compute vacuum structure in theories with symmetry breaking. Applications to \({\phi^3}\) and \({\phi^4}\) theories are discussed as illustrations and compared with variational coherent-state analyses.     

Light-Front Holography and the Light-Front Coupled-Cluster Method

We summarize the light-front coupled-cluster (LFCC) method for the solution of field-theoretic bound-state eigenvalue problems and indicate the connection with light-front holographic QCD. This includes a sample application of the LFCC method and leads to a relativistic quark model for mesons that adds longitudinal dynamics to the usual transverse light-front holographic Schrödinger equation.     

Effects of topology on the light front

We discuss how to construct theta vacua in the light-front field theories using the 1+1 dimensional Abelian Higgs model as an example. Unlike the non-gauged scalar field, zero modes of the Higgs field are in general dynamical as well as the gauge-field zero mode. While symmetry breaking is discussed in semi-classical treatment of the zero modes, the theta vacua are introduced in the quantum level by use of the large gauge symmetry.     

Vacuum structures in Hamiltonian light-front dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.     

A Light-Front Coupled Cluster Method

A new method for the nonperturbative solution of quantum field theories is described. The method adapts the exponential-operator technique of the standard many-body coupled-cluster method to the Fock-space eigenvalue problem for light-front Hamiltonians. This leads to an effective eigenvalue problem in the valence Fock sector and a set of nonlinear integral equations for the functions that define the exponential operator. The approach avoids at least some of the difficulties associated with the Fock-space truncation usually used.     

A light-front coupled-cluster method for the nonperturbative solution of quantum field theories

We propose a new method for the nonperturbative solution of quantum field theories and illustrate its use in the context of a light-front analog to the Greenberg–Schweber model. The method is based on light-front quantization and uses the exponential-operator technique of the many-body coupled-cluster method. The formulation produces an effective Hamiltonian eigenvalue problem in the valence Fock sector of the system of interest, combined with nonlinear integral equations to be solved for the functions that define the effective Hamiltonian. The method avoids the Fock-space truncations usually used in nonperturbative light-front Hamiltonian methods and, therefore, does not suffer from the spectator dependence, Fock-sector dependence, and uncanceled divergences caused by such truncations.     

The vacuum structure of light-frontφ 1+1 4 -theory

We discuss the vacuum structure ofφ ⁴-theory in 1+1 dimensions quantised on the light-frontx ⁺=0. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having longitudinal light-front momentum equal to zero, as a function of all the other modes in the theory. We analyse whether this zero mode can lead to a non-vanishing vacuum expectation value of the fieldφ and thus to spontaneous symmetry breaking. In perturbation theory, we get no symmetry breaking. If we solve the constraint, however, non-perturbatively, within a meanfield type Fock ansatz, the situation changes: while the vacuum state itself remains trivial, we find a non-vanishing vacuum expectation value above a critical coupling. Exactly the same result is obtained within a light-front Tamm-Dancoff approximation, if the renormalisation is done in the correct way.     

Method of Asymptotic Dynamics in Light-Front Field Theory

We discuss the recently proposed modified approach to asymptotic dynamics in the context of light-front field theories and apply it to light-front quantum electrodynamics (LFQED) and light-front quantum chromodynamics (LFQCD). We show that in the case of LFQED, the improved method leads to the same set of coherent states as the one obtained earlier by us using the standard Kulish and Faddeev (KF) method. However, in the case of LFQCD, the improved method leads to a set of states different from the ones obtained by using the KF method.     

AdS/QCD and Applications of Light-Front Holography

Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional physical space-time,thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD,a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time.To a first semiclassical approximation,where quantum loops and quark masses are not included,this approach leads to a single-variable light-front Schro¨dinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum.The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time.The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.We give an overview of the light-front holographic approach to strongly coupled QCD.In particular,we study the photon-to-meson transition form factors(TFFs) FMγ(Q 2) for γ→ M using light-front holographic methods.The results for the TFFs for the η and η ' mesons are also presented.Some novel features of QCD are discussed,including the consequences of confinement for quark and gluon condensates.A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.     

Varying vacuum energy of a self-interacting scalar field

Understanding mechanisms capable of altering the vacuum energy is currently of interest in field theories and cosmology. We consider an interacting scalar field and show that the vacuum energy naturally takes any value between its maximum and zero because interaction affects the number of operating field modes, the assertion that involves no assumptions or postulates. The mechanism is similar to the recently discussed temperature evolution of collective modes in liquids. The cosmological implication concerns the evolution of scalar field ?$?$ during the inflation of the Universe. ?$?$ starts with all field modes operating and maximal vacuum energy in the early inflation-dominated epoch. As a result of inflation, ?$?$ undergoes a dynamical crossover and arrives in the state with one long-wavelength longitudinal mode and small positive vacuum energy predicted to be asymptotically decreasing to zero in the late epoch. Accordingly, we predict that the currently observed cosmological constant will decrease in the future, and comment on the possibility of a cyclic Universe.     

Ward-Takahashi Identity on the Light Front

. The Ward-Takahashi identity, reflecting local gauge invariance, is perturbatively verified for a boson model in light-front field theory. A careful integration over the light-front energy, corresponding to exactly taking into account pair terms, which are the contributions of the zero longitudinal-momentum mode, is crucial to obtain this result. Furthermore, the one-loop boson form factors are calculated for arbitrary off-shell momenta. Received July 1, 1997; accepted for publication October 10, 1997     

Light-like noncommutativity,light-front quantization and new light on UV/IR mixing

We revisit the problem of quantizing field theories on noncommutative Moyal space–time with light-like   noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p⁺$p^{+}$. Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.     

Why Pair Production Cures Covariance in the Light-Front?

We show that the light-front vacuum is not trivial, and the Fock space for positive energy quanta solutions is not complete. As an example of this non triviality we have calculated the electromagnetic current for scalar bosons in the background field method were the covariance is restored through considering the complete Fock space of solutions. In this work we construct the electromagnetic current operator for a system composed of two free bosons. The technique employed to deduce these operators is through the definition of global propagators in the light front when a background electromagnetic field acts on one of the particles.     

Much ado about nothing: Vacuum and renormalization in the light-front framework

In the light-front (LF) formulation of quantum field theory, nontrivial vacuum structure can appear only in zero-modes. Integrating out zero-mode degrees of freedom leads to an effective LF Hamiltonian, which acts only on nonzero-modes and thus has a trivial vacuum, but is nevertheless equivalent to the Hamiltonian in normal coordinates (with nontrivial vacuum) since the nontrivial vacuum structure enters through the coefficients of the eff. LF Hamiltonian.     

Quarks in a constant self-dual Euclidean background field: (II). Influence on the stability of the background field

The fermionic determinant is expanded in powers of the oscillations around a semiclassical background gluon field. In the quadratic approximation, with a translation invariant (anti)self-dual background SU(2) gluon field, the changes of the zero eigenvalues are investigated in a perturbative approximation. Subtracting the field-idependent contributions, the eigenvalue of the “color-longitudinal” zero mode is unchanged while those of the “color-transverse” zero modes get positive shifts, suggesting a further stabilization of the gluonic oscillations.     

Dynamical instability induced by the zero mode under symmetry breaking external perturbation

A complex eigenvalue in the Bogoliubov–de Gennes equations for a stationary Bose–Einstein condensate in the ultracold atomic system indicates the dynamical instability of the system. We also have the modes with zero eigenvalues for the condensate, called the zero modes, which originate from the spontaneous breakdown of symmetries. Although the zero modes are suppressed in many theoretical analyses, we take account of them in this paper and argue that a zero mode can change into one with a pure imaginary eigenvalue by applying a symmetry breaking external perturbation potential. This emergence of a pure imaginary mode adds a new type of scenario of dynamical instability to that characterized by the complex eigenvalue of the usual excitation modes. For illustration, we deal with two one-dimensional homogeneous Bose–Einstein condensate systems with a single dark soliton under a respective perturbation potential, breaking the invariance under translation, to derive pure imaginary modes.     

Electrogravitational instability of cylindrical interface acted upon by a varying electric field

The electrodynamic instability of a self-gravitating dielectric fluid penetrated by a uniform axial electric field surrounded by a self-gravitating vacuum pervaded by a varying electric field is investigated. A general eigenvalue relation valid to all possible (symmetric and asymmetric) modes of perturbation for all (short and long) wavelengths is derived and discussed in detail. The model is gravitationally stable to the pure asymmetric disturbances modes while to symmetric modes it is as if the longitudinal wavenumber normalized with respect to the jet radius is equal to or greater than 1.0668 and vice versa. The axial electric fields pervaded interior and exterior to the cylinder are stabilizing for all disturbances modes according to some restrictions. The transverse varying electric field is purely stabilizing in the symmetric disturbance for all wavelengths, while it is stabilizing in the asymmetric disturbance under some restrictions. The electrodynamic force has a strong stabilizing influence in the symmetric mode and can suppress the gravitational instability above a certain value of the basic electric field.     

INSTABILITY OF THE MEAN FIELD VACUUM IN LATTICE GAUGE THEORIES

We calculate the interaction energy between heavy quark pair in the Hamiltonian formulation of lattice gauge theories. Mean field-variational calculations show that the upper limit of the string tension is zero in the weak coupling region if we use approximate vacuum state of the mean field type. The mean field vacuum is unstable against forming closed flux loops.     

Relativistic Covariance of Light-Front Few-Body Systems in Hadron Physics

We study the light-front covariance of a vector-meson decay constant using a manifestly covariant fermion field theory model in (3 + 1) dimensions. The light-front zero-mode issues are analyzed in terms of polarization vectors and method of identifying the zero-mode operator and of obtaining the light-front covariant decay constant is discussed.