Quantum Field Description Research Articles

Gauge invariance, gauge field quantization, and renormalization in autoregularization

Autoregularization, a new divergence-free framework for calculating scattering amplitudes, uses a Lorentz-invariant scale harvested from the kinematics of a scattering process to regularize the amplitude of the process [N. Prabhu, .]. Preliminary validation studies show that autoregularization’s predictions are in good agreement with experimental data—across several scattering processes and a wide range of energy scales. Further, tree-level calculation of the vacuum energy density of the free fields in the Standard Model, using autoregularization, is shown to yield a value that is smaller than the current estimate of the cosmic critical density. In this paper, we prove that the scattering amplitudes in QED, calculated using autoregularization, are gauge invariant. Our proof, which is valid both for autoregularization and current theory, is stronger in that it shows the amplitude of every Feynman diagram is gauge invariant in contrast to previous proofs, which establish gauge invariance only for sum of amplitudes of Feynman diagrams of a process. Next, we show that—unlike in the standard quantization framework, which requires modification of both the quantization framework itself as well as the Lagrangian in order to quantize gauge fields in covariant gauge—in autoregularization the gauge field in QED can be quantized, in covariant gauge, without modifying the standard quantization procedure or the Lagrangian and without introducing the ghost field. Finally, we illustrate renormalization based on autoregularization up to 1-loop in φ4 theory. Since perturbative corrections are finite in autoregularization, the counterterms are not designed to remove divergences but to implement renormalization prescriptions at every order of perturbation. We also derive the renormalization group equation (RGE). Unlike in some regularization schemes (such as dimensional regularization), in which the physical meaning of the fictitious scale introduced by regularization is unclear, in autoregularization the scale in RGE has a transparent physical meaning—it is the Lorentz-invariant kinematic scale of the scattering process of interest. The increasing simplifications resulting within autoregularization and the agreement between its predictions and experimental data, together with the underlying thermodynamic argument, which shows that the framework is essential for a complete description of quantum fields, all converge to suggest that autoregularization provides the proper framework for the description of quantum fields. Published by the American Physical Society 2024

Radiative properties of an artificial atom coupled to a Josephson-junction array

We study the radiative properties -- the Lamb shift, Purcell decay rate and the spontaneous emission dynamics -- of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to non-perturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson junction array (JJA). As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are non-trivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode non-perturbative regime. This modal framework generalizes the normal mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high impedance Josephson junction arrays.

Quantization of interacting Galilean field theories

We present the quantum field description of Galilean electrodynamics minimally coupled to massless Galilean fermion in (3 + 1)-dimensions. At classical level, the Lagrangian is obtained as a null reduction of a relativistic theory in one higher dimension. We use functional techniques to develop the quantum field description of the theory. Quantum corrections to the propagators and vertex are obtained upto first order and the theory is found to be renormalizable to this order. The beta function of the theory is found to grow linearly; the theory is not asymptotically free.

Quantum control with quantum light of molecular nonadiabaticity

Coherent control experiments in molecules are often done with shaped laser fields. The electric field is described classically and control over the time evolution of the system is achieved by shaping the laser pulses in the time or frequency domain. Moving on from a classical to a quantum description of the light field allows to engineer the quantum state of light to steer chemical processes. The quantum field description of the photon mode allows to manipulate the light-matter interaction directly in phase-space. In this paper we will demonstrate the basic principle of coherent control with quantum light on the avoided crossing in lithium fluoride. Using a quantum description of light together with the nonadiabatic couplings and vibronic degrees of freedoms opens up new perspective on quantum control. We show the deviations from control with purely classical light field and how back-action of the light field becomes important in a few photon regime.

Ultrafast dynamics in the vicinity of quantum light-induced conical intersections

Nonadiabatic effects appear due to avoided crossings or conical intersections (CIs) that are either intrinsic properties in field-free space or induced by a classical laser field in a molecule. It was demonstrated that avoided crossings in diatomics can also be created in an optical cavity. Here, the quantized radiation field mixes the nuclear and electronic degrees of freedom creating hybrid field-matter states called polaritons. In the present theoretical study we go further and create CIs in diatomics by means of a radiation field in the framework of cavity quantum electrodynamics. By treating all degrees of freedom, that is the rotational, vibrational, electronic and photonic degrees of freedom on an equal footing we can control the nonadiabatic quantum light-induced dynamics by means of CIs. First, the pronounced difference between the the quantum light-induced avoided crossing and the CI with respect to the nonadiabatic dynamics of the molecule is demonstrated. Second, we discuss the similarities and differences between the classical and the quantum field description of the light for the studied scenario.

Quantum superposition of massive objects and the quantization of gravity

We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies ("particles") under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice's particle) and vacuum fluctuations of the electromagnetic field (which limits Bob's ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We correct an error in the analysis of Mari et al. and of Baym and Ozawa, who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.

On the precanonical structure of the Schrödinger wave functional

We show that the Schr\"odinger wave functional may be obtained as the product integral of precanonical wave functions on the space of field and space-time variables. The functional derivative Schr\"odinger equation underlying the canonical field quantization is derived from the partial derivative covariant analogue of the Schr\"odinger equation, which appears in the precanonical field quantization based on the De Donder-Weyl generalization of the Hamiltonian formalism for field theory. The representations of precanonical quantum operators typically contain an ultraviolet parameter $\varkappa$ of the dimension of the inverse spatial volume. The transition from the precanonical description of quantum fields in terms of Clifford-valued wave functions and partial derivative operators to the standard functional Schr\"odinger representation obtained from canonical quantization is accomplished if $\frac{1}{\varkappa}\rightarrow 0$ and $\frac{1}{\varkappa}\gamma_0$ is mapped to the infinitesimal spatial volume element $\mathrm{d}\mathbf{x}$. Thus the standard QFT obtained via canonical quantization corresponds to the quantum theory of fields derived via precanonical quantization in the limiting case of an infinitesimal value of the parameter $\frac{1}{\varkappa}$.

Unstable states in quantum theory

Various approaches to the problem of describing unstable particles are reviewed. Fundamental problems that arise in quantum field description of these particles and the ways of their solution are considered. Among them, there is an approach related to the notion of the smeared (continuous) mass, which originates from the finite lifetime of unstable particles. The quantum field model of unstable particles with smeared mass, which is built upon two basic axiomatic elements, is considered in detail. The basic processes with unstable particles (decay and scattering) are considered within the framework of the model and the formalism for describing physical characteristics of those processes is developed. The model is successfully applied to describing the processes of pair and triple boson production at the linear collider, top quark pair production, and certain hadronic decays. Based on this model, the factorization method is developed, which allows a description of complicated and multistep scattering and decay processes with unstable particles to be considerably simplified.

Time Crystals in Ultracold Matter

We consider the formation of time crystals in a gas of laser-cooled atoms. We show that the phonon frequency is shifted inside a time crystal, and the phonon backscattering resulting from a temporal Bragg diffraction can be observed. A quantum-field description allows us to demonstrate that these effects are accompanied by emission of the phonon pairs from vacuum. The same description can be used for the dynamical Casimir effect, which, in some sense, is as a special case of the time crystal with similar quantum vacuum properties. Due to its low temperature and low noise level, a gas of ultracold atoms seems promising for experimental studies in quantum vacuum phenomena, such as those associated with time crystals.

Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons

Quantum many-body systems can have phase transitions even at zero temperature; fluctuations arising from Heisenberg's uncertainty principle, as opposed to thermal effects, drive the system from one phase to another. Typically, during the transition the relative strength of two competing terms in the system's Hamiltonian changes across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry, a novel type of quantum phase transition may be induced and driven by an arbitrarily weak perturbation to the Hamiltonian. Here we observe such an effect--the sine-Gordon quantum phase transition from a superfluid Luttinger liquid to a Mott insulator--in a one-dimensional quantum gas of bosonic caesium atoms with tunable interactions. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model. We trace the phase boundary all the way to the weakly interacting regime, where we find good agreement with the predictions of the one-dimensional Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality and transport phenomena beyond Hubbard-type models in the context of ultracold gases.

Uniqueness of the Fock quantization of a free scalar field onS1with time dependent mass

We analyze the quantum description of a free scalar field on the circle in the presence of an explicitly time dependent potential, also interpretable as a time dependent mass. Classically, the field satisfies a linear wave equation of the form $\ddot{\xi}-\xi"+f(t)\xi=0$. We prove that the representation of the canonical commutation relations corresponding to the particular case of a massless free field ($f=0$) provides a unitary implementation of the dynamics for sufficiently general mass terms, $f(t)$. Furthermore, this representation is uniquely specified, among the class of representations determined by $S^1$-invariant complex structures, as the only one allowing a unitary dynamics. These conclusions can be extended in fact to fields on the two-sphere possessing axial symmetry. This generalizes a uniqueness result previously obtained in the context of the quantum field description of the Gowdy cosmologies, in the case of linear polarization and for any of the possible topologies of the spatial sections.

Criticality in a Vlasov-Poisson system: A fermioniclike universality class

A model Vlasov-Poisson system is simulated close to the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power-law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality d=5 below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead, it corresponds to the propagator for the fermionic vector field and to the upper critical dimensionality d(c) = 2. This suggests criticality of collisionless Vlasov-Poisson systems corresponds to a universality class analogous to that of critical phenomena of a fermionic quantum field description.

All-optical devices based on three-wave mixing for logic and information processing

A method of creating all-optical devices for logic information processing is presented. The mechanism is based on virtual photon interaction in quantum field description, or dipole moment interaction in classical description. The device consists of two optical information bits channels and one optical bits channel of logic commands like AND, NOT, OR. A variety of logic operations can be achieved on one optical setup by polarization change of the logic bits which determines the logic commands. I present another application for the method as an information channels selector.

A quantum trajectory analysis of the one-atom micromaser

In this paper results are reported for the application of the quantum trajectory method to analysing the dynamics of the micromaser. The master equation for the cavity field is derived by a method which highlights the close relationship between the quantum trajectory method and the usual model for the one-atom micromaser. Possible quantum trajectory unravellings of the micromaser dynamics are discussed, and a simple number-state unravelling is described and used to generate simulations from which the cavity-field intensity correlation function is calculated. Attention is principally confined to the case of a Poissonian atomic beam, though a method of dealing with the non-Markovian master equation obtained for non-Poissonian beams is also examined. A formal theory of atomic detection analogous to the Glauber - Kelly - Kleiner theory of photodetection is proposed, based on a quantum-field description of the atomic beam. This theory is used to establish the connection between the atomic detection record obtained by continuous monitoring of the atoms leaving the cavity and the quantum trajectories followed by the cavity field. Results obtained by other treatments of atomic detection are regained. A classical correlation function obtained from the detection record of ground-state atoms emerging from a micromaser cavity is then shown, by use of a quantum trajectory analysis, to be identical to the cavity field intensity correlation function, apart from shot-noise-type contributions, provided the cavity reservoir is at zero temperature.

Fermion localization and causality

The velocity of a fermion (neutrino) propagation from its source to its detector is investigated. It is shown that a simple approach to the problem in terms of the quantum packet spreading (Hegerfeldtet al.) is not applicable because the fermion cannot be localized in a bounded space region. Another approach is elaborated which uses relativistic quantum field description of the fermion source and detector. It is demonstrated that the velocity of the fermion propagation does not exceed the light velocityc within the precision of the source and detector localization.

A geometrical approach to external potential problems in quantum field theory

A geometrical framework for obtaining the5-operator description of quantum fields interacting with external potentials (including gravitation) is presented. An approach to quantum theory of mutually interacting Bose fields is suggested.