A quantization of the electromagnetic field

1983 ◽  
Vol 61 (8) ◽  
pp. 1172-1183
Author(s):  
Anton Z. Capri ◽  
Gebhard Grübl ◽  
Randy Kobes
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Free Field ◽  
External Source ◽  
Field Level ◽  
Manifest Covariance ◽  
The One ◽  
Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

The free field

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Gauge Invariance ◽  
Maxwell Equations ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Initial Conditions ◽  
Free Field ◽  
Maxwell Theory ◽  
Gauge Invariant ◽  
Massive Vector ◽  
The One

This chapter studies the structure of Maxwell’s equations in a vacuum and the action from which they are derived, while emphasizing the consequences of their gauge invariance. Gauge invariance, on the one hand, allows one of the components of the magnetic potential to be chosen freely. Here, the chapter shows how the gauge-invariant version of the Maxwell equations in the vacuum can also be derived directly by extremizing. On the other hand, the chapter argues that gauge invariance imposes a constraint on the initial conditions such that in the end the general solution has only two ‘degrees of freedom’. Finally, the chapter develops the Hamiltonian formalisms in the Maxwell theory and compares them to the formalisms using non-gauge-invariant or massive vector fields.

scholarly journals Monodromy defects in free field theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenzo Bianchi ◽  
Adam Chalabi ◽  
Vladimír Procházka ◽  
Brandon Robinson ◽  
Jacopo Sisti
Keyword(s):  
Entanglement Entropy ◽  
Free Field ◽  
Operator Product ◽  
Dirac Fermions ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Defect Operator ◽  
Crucial Information ◽  
The One ◽  
Group Flow

Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture

2021 ◽  
pp. 2150142
Author(s):  
David Montenegro ◽  
B. M. Pimentel
Keyword(s):  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Mass Shell ◽  
Natural Extension ◽  
Quantum Model ◽  
Covariant Quantization ◽  
Heisenberg Picture ◽  
Maxwell Electrodynamics ◽  
Loop Amplitude ◽  
The One

We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

Similarities and Differences between Performers and Observers in Processing Auditory Action Consequences: Evidence from Simultaneous EEG Acquisition

2020 ◽  
pp. 1-12
Author(s):  
Marta Ghio ◽  
Sophie Egan ◽  
Christian Bellebaum
Keyword(s):  
Social Environment ◽  
Sensory Processing ◽  
Action Observation ◽  
Methodological Approach ◽  
External Source ◽  
Similarities And Differences ◽  
The One ◽  
Physically Identical ◽  
Healthy Participants ◽  
Predictive Mechanisms

In our social environment, we easily distinguish stimuli caused by our own actions (e.g., water splashing when I fill my glass) from stimuli that have an external source (e.g., water splashing in a fountain). Accumulating evidence suggests that processing the auditory consequences of self-performed actions elicits N1 and P2 ERPs of reduced amplitude compared to physically identical but externally generated sounds, with such reductions being ascribed to neural predictive mechanisms. It is unexplored, however, whether the sensory processing of action outcomes is similarly modulated by action observation (e.g., water splashing when I observe you filling my glass). We tested 40 healthy participants by applying a methodological approach for the simultaneous EEG recording of two persons: An observer observed button presses executed by a performer in real time. For the performers, we replicated previous findings of a reduced N1 amplitude for self- versus externally generated sounds. This pattern differed significantly from the one in observers, whose N1 for sounds generated by observed button presses was not attenuated. In turn, the P2 amplitude was reduced for processing action- versus externally generated sounds for both performers and observers. These findings show that both action performance and observation affect the processing of action-generated sounds. There are, however, important differences between the two in the timing of the effects, probably related to differences in the predictability of the actions and thus also the associated stimuli. We discuss how these differences might contribute to recognizing the stimulus as caused by self versus others.

Quantisation of the Electromagnetic Field and Spontaneous Photon Emission

2021 ◽  
pp. 4-23
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Electromagnetic Field ◽  
Excited State ◽  
Physical Interpretation ◽  
Gauge Invariance ◽  
Photon Emission ◽  
Perturbation Expansion ◽  
Atomic State ◽  
Abstract Concepts ◽  
Free Electromagnetic Field ◽  
Physical Result

We develop the method of canonical quantisation for the case of the free electromagnetic field. We choose the Coulomb gauge, which has a simpler physical interpretation. We introduce the creation and annihilation operators in this framework. The formalism is applied to the problem of spontaneous emission of radiation from an excited atomic state at first order in the perturbation expansion. This allows us to obtain a concrete physical result, namely the computation of an excited state decay rate, and, at the same time, have a first look at abstract concepts, such as gauge invariance and renormalisation.

Regularity of weak solutions for the relativistic Vlasov–Maxwell system

2018 ◽  
Vol 15 (04) ◽  
pp. 693-719 ◽  
Author(s):  
Nicolas Besse ◽  
Philippe Bechouche
Keyword(s):  
Electromagnetic Field ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Regularity Of Solutions ◽  
Maxwell System ◽  
Smoothing Effect ◽  
Regular Solutions ◽  
Low Velocity ◽  
Regularity Of Weak Solutions ◽  
The One

We investigate the regularity of weak solutions of the relativistic Vlasov–Maxwell system by using Fourier analysis and the smoothing effect of low velocity particles. This smoothing effect has been used by several authors (see Glassey and Strauss 1986; Klainerman and Staffilani, 2002) for proving existence and uniqueness of [Formula: see text]-regular solutions of the Vlasov–Maxwell system. This smoothing mechanism has also been used to study the regularity of solutions for a kinetic transport equation coupled with a wave equation (see Bouchut, Golse and Pallard 2004). Under the same assumptions as in the paper “Nonresonant smoothing for coupled wave[Formula: see text]+[Formula: see text]transport equations and the Vlasov–Maxwell system”, Rev. Mat. Iberoamericana 20 (2004) 865–892, by Bouchut, Golse and Pallard, we prove a slightly better regularity for the electromagnetic field than the one showed in the latter paper. Namely, we prove that the electromagnetic field belongs to [Formula: see text], with [Formula: see text].

scholarly journals Derivative expansion for the one-loop effective Lagrangian in QED

1996 ◽  
Vol 74 (5-6) ◽  
pp. 282-289 ◽  
Author(s):  
V. P. Gusynin ◽  
I. A. Shovkovy
Keyword(s):  
Electromagnetic Field ◽  
Field Strength ◽  
External Field ◽  
Explicit Expression ◽  
Derivative Expansion ◽  
Effective Lagrangian ◽  
Constant Electromagnetic Field ◽  
The One ◽  
Derivatives Of

The derivative expansion of the one-loop effective Lagrangian in QED4 is considered. The first term in such an expansion is the famous Schwinger result for a constant electromagnetic field. In this paper we give an explicit expression for the next term containing two derivatives of the field strength Fμν. The results are presented for both fermion and scalar electrodynamics. Some possible applications of an inhomogeneous external field are pointed out.

scholarly journals THERMAL FIELD THEORY IN A WIRE: APPLICATIONS OF THERMAL FIELD THEORY METHODS TO THE PROPAGATION OF PHOTONS IN A ONE-DIMENSIONAL PLASMA

2011 ◽  
Vol 26 (32) ◽  
pp. 5387-5402 ◽  
Author(s):  
JOSÉ F. NIEVES
Keyword(s):  
Field Theory ◽  
Thermal Field Theory ◽  
Thermal Field ◽  
Free Field ◽  
Dynamical Variable ◽  
Effective Field ◽  
Dispersion Relations ◽  
One Dimensional ◽  
Self Energy ◽  
The One

The Thermal Field Theory methods are applied to calculate the dispersion relation of the photon propagating modes in a strictly one-dimensional (1D) ideal plasma. The electrons are treated as a gas of particles that are confined to a 1D tube or wire, but are otherwise free to move, without reference to the electronic wave functions in the coordinates that are transverse to the idealized wire, or relying on any features of the electronic structure. The relevant photon dynamical variable is an effective field in which the two space coordinates that are transverse to the wire are collapsed. The appropriate expression for the photon free-field propagator in such a medium is obtained, the one-loop photon self-energy is calculated and the (longitudinal) dispersion relations are determined and studied in some detail. Analytic formulas for the dispersion relations are given for the case of a degenerate electron gas, and the results differ from the long-wavelength formula that is quoted in the literature for the strictly 1D plasma. The dispersion relations obtained resemble the linear form that is expected in realistic quasi-1D plasma systems for the entire range of the momentum, and which have been observed in this kind of system in recent experiments.

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