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.     

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.     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.     

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.     

Spin Operator Matrix Elements in the Superintegrable Chiral Potts Quantum Chain

We derive spin operator matrix elements between general eigenstates of the superintegrable ℤ _N -symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum chain in a transverse field (N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the Separation of Variables method.     

Finite-Temperature Field Theory on the Light Front

The formulation of statistical physics using light-front quantization, instead of conventional equal-time boundary conditions, has important advantages for describing relativistic statistical systems, such as heavy ion collisions. We develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. First, we construct the most general form of the statistical operator allowed by the Poincaré algebra. In light-front quantization, the Green’s functions of a quark in a medium can be defined in terms of just two-component spinors and do not lead to doublers in the transverse directions. Since the theory is non-local along the light cone, we use causality arguments to construct a solution to the related zero-mode problem. A seminal property of light-front Green’s functions is that they are related to parton densities in coordinate space. Namely, the diagonal and off-diagonal parton distributions measured in hard scattering experiments can be interpreted as light-front density matrices.     

Zero modes in the light-front coupled-cluster method

The light-front coupled-cluster (LFCC) method is a technique for solving Hamiltonian eigenvalue problems in light-front-quantized field theories. Its primary purpose is to provide a systematic sequence of solvable approximations to the original eigenvalue problem without the truncation of Fock space. Here we discuss the incorporation of zero modes, modes of zero longitudinal momentum, into the formalism of the method. Without zero modes, the light-front vacuum is trivial, and the vacuum expectation value of the field is always zero. The LFCC method with zero modes provides for vacuum structure, in the form of a generalized coherent state of zero modes, as is illustrated here in two-dimensional model field theories.     

Cubic algebra and averaged Hamiltonian for the resonance 3: (?1) Penning-ioffe trap

For the 3: (?1) resonance Penning trap, we describe the algebra of symmetries which turns out to be a non-Lie algebra with cubic commutation relations. The irreducible representations and coherent states of this algebra are constructed explicitly. The perturbing inhomogeneous magnetic field of Ioffe type, after double quantum averaging, generates an effective Hamiltonian of the trap. In the irreducible representation, this Hamiltonian becomes a second-order ordinary differential operator of the Heun type.     

On Dynamics of 5D superconformal theories

5D superconformal theories involve vacuum valleys characterized in the simplest case by the vacuum expectation value of the real scalar field σ. If 〈σ〉 ≠ 0, conformal invariance is spontaneously broken and the theory is not renormalizable. In the conformally invariant sector 〈σ〉 = 0, the theory is intrinsically nonperturbative. We study classical and quantum dynamics of this theory in the limit when field dependence of the spatial coordinates is disregarded. The classical trajectories “fall” on the singularity at σ = 0. The quantum spectrum involves ghost states with negative energies unbounded from below, but such states fail to form complete 16-plets as is dictated by the presence of four complex supercharges and should be rejected for that reason. Physical excited states come in supermultiplets and have all positive energies.We conjecture that the spectrum of the complete field theory Hamiltonian also becomes positive definite (ghost-free) when invoking supersymmetry considerations.We speculate that the ghosts in higher derivative supersymmetric field theories are exterminated by a similar mechanism. The text was submitted by the author in English. On leave of absence from ITEP, Moscow, Russia     

Generalized Poisson algebras and Hamiltonian dynamics

Hamiltonian dynamics can be formulated entirely in terms of a Poisson manifold, that is, one for which the algebra of smooth functions is a Poisson algebra. The latter is a commutative associative algebraA together with a skew-symmetric bracket which is a derivation onA. It is shown that a Poisson algebra can be generalized by replacingA by algebras which do not necessarily commute. These allow for algebraic generalizations of Hamiltonian dynamics in both classical and quantum forms. Particular examples are models of classical and quantum electrons.     

Spontaneous emission of light from atoms: the model

We investigate (non‐relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two‐level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal‐coupling Hamiltonian, with the A² term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra‐type equation which governs the time evolution of the amplitude of the excited state. The two‐point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.     

New Results in Light-Front Phenomenology

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. In this talk I review the theoretical methods and constraints which can be used to determine these central elements of QCD phenomenology. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and define a kinematical definition of angular momentum. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in four-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The nonperturbative Fock-state wavefunctions contain intrinsic gluons, and sea quarks at any scale Q with asymmetries such as . Intrinsic charm and bottom quarks appear at large x in the light-front wavefunctions since this minimizes the invariant mass and off-shellness of the higher Fock state. In the case of nuclei, the Fock state expansion contains “hidden color” states which cannot be classified in terms of nucleonic degrees of freedom. I also briefly review recent analyses which show that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.Work supported by Department of Energy contract DE-AC02-76SF00515     

Macroscopic Superpositions and Entanglement of Mesoscopic Squeezed Vacuum States in Dissipative Cavity QED System

A scheme has been proposed for generating the macroscopic superpositions and the entanglement between the mesoscopic squeezed vacuum states by considering the two-photon interaction of N two-level atoms in a dissipative cavity with high quality factor assisted by a strong driving field. A number of multiparty entangled states between the atoms and the squeezed vacuum states, among the atoms, and among the squeezed vacuum states, can be prepared by virtue of a specific choice of the cavity detuning and the detuning of applied coherent field under the dissipation condition. The corresponding analytical expressions of the influence can be given. Moreover, we can also give a series of macroscopic entangled states between the usual coherent states and the squeezed vacuum states using the combination of the dissipative one-photon interaction Hamiltonian with the dissipative two-photon interaction Hamiltonian. We also discuss the experimental feasibility. Our scheme can be realized in the current techniques on the cavity QED.     

通过基矢光前量子化方法对π介子的研究

为研究介子的性质,通过基矢光前量子化方法获得介子的光前波函数。基失光前量子化是一种在哈密顿量体系下基于量子场论的非微扰方法。在哈密顿量中我们考虑了动能项、基于全息色动力学的横向禁闭势、与横向禁闭势互补的纵向禁闭势和基于QCD的夸克-胶子相互作用。我们的基矢空间包括最低阶的两个Fock空间,即领头阶■与次领头阶■。根据所得的光前波函数我们计算了介子衰变常数以及(基于领头Fock空间的)电磁半径,这些结果与粒子数据手册(PDG)上的结果相近。此外,我们计算了(基于领头Fock空间的)介子部分子分布,QCD演化后,与原先的结果相近(蓝江山等,Phys Rev Lett,2 019,122:172 001.),能够很好地描述费米国家实验室(FNAL)与欧洲核子中心(CERN)的实验数据。     

Second quantized scalar QED in homogeneous time-dependent electromagnetic fields

We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.     

QCD on the Light-Front

Light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x ⁺ = x ⁰ + x ³, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian H _LF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of H _LF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable \({\zeta^2=b^2_\perp x(1-x)}\) , which is conjugate to the invariant mass squared \({{M^2_{q\bar q}}}\) . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories \({M^2(n, L, S) = 4\kappa^2( n+L +S/2)}\) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter \({\kappa}\) appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS₅ space with a unique dilaton profile to QCD (3 + 1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.     

Quantum symmetries and thermal field dynamics

In Thermal Field Dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenberg bialgebra. The relationship between quantum symmetries and doublings is discussed.     

Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

HeiddenSL(n) symmetry in conformal field theories

We prove that an irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of theSL(2, ) current algebra by putting a constraint on the latter using the Becchi-Rouet-Stora-Tyutin formalism. Thus there is aSL(2, ) symmetry in the Virasoro algebra, but it is gauged and hidden. This construction of the Virasoro algebra is the quantum analogue of the Hamiltonian reduction. We then are naturally lead to consider a constrainedSL(2, ) Wess-Zumino-Witten model. This system is also related to quantum field theory of coadjoint orbit of the Virasoro group. Based on this result, we present a canonical derivation of theSL(2, ) current algebra in Polyakov's theory of two-dimensional gravity; it is a manifestation of theSL(2, ) symmetry in conformal field theory hidden by the quantum Hamiltonian reduction. We also discuss the quantum Hamiltonian reduction of theSL(2, ) current algebra and its relation to theW _n -algebra of Zamolodchikov. This makes it possible to define a natural generalization of the geometric action for theW _n -algebra despite its non-Lie-algebraic nature.This paper is dedicated to the memory of Vadik G. Knizhnik     

Electron in a transverse harmonic cavity

Recent experiments with heavy ions and planned experiments with ultraintense lasers require nonperturbative solutions to quantum field theory for predicting and interpreting the results. To propel this theoretical direction, we solve the nonperturbative problem of an electron in a strong transverse confining potential using Hamiltonian light-front quantum field theory. We evaluate both the invariant mass spectra and the anomalous magnetic moment of the lowest state for this two-scale system. The weak external field limit of the anomalous magnetic moment agrees with the result of QED perturbation theory within the anticipated accuracy.