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A correspondence of classical to quantum physics studied by Schr\"{o}\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This correspondence provides appropriate nonrelativistic classical interpretations to realizations of relativistic quantum physics that are incompatible with the canonical formalism. Using this correspondence, Newtonian mechanics for a $1/r$ potential provides approximations for the dynamics of nonrelativistic classical particle states within unconstrained quantum field theory (UQFT).

We present a unified description of zitterbewegung-like phenomena for electron and hole systems showing Rashba spin splitting as well as for electrons in single-layer and bilayer graphene. The former class of systems can be interpreted as "nonrelativistic" whereas the latter are often called "ultrarelativistic" so that our unified description indicates an interesting connection between these two opposite limits.

The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum Field Theory but less well known outside this community. The paper is intended as a concise survey of some selected aspects of relativistic quantum physics, in particular regarding localization and entanglement.

We use the laws of relativistic physics to show that classically motivated counterfactual statements are inadequate when discussing the principles of quantum physics and that EPR style arguments against state reduction are incorrect.

A representation of the quadratic Dirac equation and the Maxwell equations in terms of the three-dimensional universal complex Clifford algebra is given. The investigation considers a subset of the full algebra, which is isomorphic to the Baylis algebra. The approach is based on the two Casimir operators of the Poincare group, the mass operator and the spin operator, which is related to the Pauli-Lubanski vector. The extension to spherical symmetries is discussed briefly. The structural difference to the Baylis algebra appears in the shape of the hyperbolic unit, which plays an integral part in this formalism.

We discuss the evolution of the Universe from what might be called its quantum origin. We apply the uncertainty principle to the origin of the Universe with characteristic time scale equal to the Planck time to obtain its initial temperature and density. We establish that the subsequent evolution obeying the Einstein equation gives the present temperature of the microwave background close to the observed value. The same origin allows the possibility that the Universe started with exactly the critical density, Omega =1, and remained at the critical density during evolution. Many other important features of the observed Universe, including homogeneity and isotropy, Hubble's constant at origin, its minimum age, present density etc. are all predictions of our theory. We discuss also the testability of our theory.

We present a consistent and comprehensive treatise on the foundations of the extended Hamilton-Lagrange formalism--where the dynamical system is parameterized along a general system evolution parameter $s$, and the time $t$ is treated as a dependent variable $t(s)$ on equal footing with all other configuration space variables $q^{i}(s)$. In the action principle, the conventional classical action $L dt$ is then replaced by the generalized action $L_{\e}ds$, with $L$ and $L_{\e}$ denoting the conventional and the extended Lagrangian, respectively. It is shown that a unique correlation of $L_{\e}$ and $L$ exists if we refrain from performing simultaneously a transformation of the dynamical variables. With the appropriate correlation of $L_{\e}$ and $L$ in place, the extension of the formalism preserves its canonical form. In the extended formalism, the dynamical system is described as a constrained motion within an extended space. We show that the value of the constraint and the parameter $s$ constitutes an additional pair of canonically conjugate variables. In the corresponding quantum system, we thus encounter an additional uncertainty relation. We derive the extended Lagrangian $L_{\e}$ of a classical relativistic point particle in an external electromagnetic field and show that the generalized path integral approach yields the Klein-Gordon equation as the corresponding quantum description. We furthermore derive the space-time propagator for a free relativistic particle from its extended Lagrangian $L_{\e}$. These results can be regarded as the proof of principle of the relativistic generalization of Feynman's path integral approach to quantum physics.

Volume 1 of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a uniqu

We develop a general formalism for a non-perturbative treatment of harmonic-oscillator particle detectors in relativistic quantum field theory using continuous-variables techniques. By means of this we forgo perturbation theory altogether and reduce the complete dynamics to a readily solvable set of first-order, linear differential equations. The formalism applies unchanged to a wide variety of physical setups, including arbitrary detector trajectories, any number of detectors, arbitrary time-dependent quadratic couplings, arbitrary Gaussian initial states, and a variety of background spacetimes. As a first set of concrete results, we prove non-perturbatively--and without invoking Bogoliubov transformations--that an accelerated detector in a cavity evolves to a state that is very nearly thermal with a temperature proportional to its acceleration, allowing us to discuss the universality of the Unruh effect. Additionally we quantitatively analyze the problems of considering single-mode approximations in cavity field theory and show the emergence of causal behaviour when we include a sufficiently large number of field modes in the analysis. Finally, we analyze how the harmonic particle detector can harvest entanglement from the vacuum. We also study the effect of noise in time dependent problems introduced by suddenly switching on the interaction versus ramping it up slowly (adiabatic activation).

I discuss topics in Particle Physics applying the novel ontological formulation of Relativistic Quantum Field Theory due to David Bohm. I argument that particle physicists might too benefit from this truly novel way of thinking Physics.

We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly-coupled to a resonator field mode can be used to simulate the dynamics of the Dirac equation and Klein paradox in all regimes. Using the same setup we also propose the implementation of the Foldy-Wouthuysen canonical transformation, after which the time derivative of the position operator becomes a constant of the motion.

We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural Theories", that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors and so on). It is discussed how the use of Poincare'-Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as "generators of Noether symmetries", energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-called ADM laws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation "`a la Palatini" and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero-Immirzi connections).

In Bell inequality tests, the evolution of the wavefunction is not covariant, i.e. not invariant under velocity boost that change the time ordering of events, but the laws that govern the probability distribution of possible results are. In this note I investigate what this could mean and whether there could be some covariant "real quantum stuff". This clarifies the implication of the Free Will Theorem and of relativistic spontaneous localization models based on the flash ontology (rGRWf). Some implications for the concept of time(s) are spelled out.

A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant spinors, field operators, propagators and model interactions. Guided by an approach originally proposed by Weinberg, we construct from group theoretical arguments the (j,0)+(0,j) covariant spinors and the field operators for a massive particles. Specific examples are worked out in the familiar language of the Bjorken and Drell text for the case of the (1,0)+(0,1), (3/2,0)+(0,3/2) and (2,0)+(0,2) matter fields. The m\to 0 limit of the covariant spinors is shown to have the expected structure. The algebra of the \gamma^{\mu\nu} matrices associated with the (1,0)+(0,1) matter fields is presented, and the conserved current derived. The procedure readily extends to higher spins. The causality problem associated with the j\ge 1 wave equations is discussed in detail and a systematic procedure to construct causal propagators is provided. As an example a spin two wave equation satisfied by the (2,0)+(0,2), covariant spinors is found to support not only ten correct and causal solutions, but also thirty physically unacceptable acausal solutions. However, we demonstrate how to construct the Feynman propagator for the higher spin particles directly from the spinors and thus avoid the shortcomings of the wave equation in building a phenomenology. The same exercise is repeated for the (1,0)+(0,1) and (3/2,0)+(0,3/2) matter fields, and the same conclusions obtained. Massless limit is discussed in detail. (Typos uncorrected, Part of the work published and extended in several journal articles, for an important correction see physics/9702005).

A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant spinors, field operators, propagators and model interactions. Guided by an approach originally proposed by Weinberg, we construct from group theoretical arguments the (j,0)+(0,j) covariant spinors and the field operators for a massive particles. Specific examples are worked out in the familiar language of the Bjorken and Drell text for the case of the (1,0)+(0,1), (3/2,0)+(0,3/2) and (2,0)+(0,2) matter fields. The m\to 0 limit of the covariant spinors is shown to have the expected structure. The algebra of the \gamma^{\mu\nu} matrices associated with the (1,0)+(0,1) matter fields is presented, and the conserved current derived. The procedure readily extends to higher spins. The causality problem associated with the j\ge 1 wave equations is discussed in detail and a systematic procedure to construct causal propagators is provided. As an example a spin two wave equation satisfied by the (2,0)+(0,2), covariant spinors is found to support not only ten correct and causal solutions, but also thirty physically unacceptable acausal solutions. However, we demonstrate how to construct the Feynman propagator for the higher spin particles directly from the spinors and thus avoid the shortcomings of the wave equation in building a phenomenology. The same exercise is repeated for the (1,0)+(0,1) and (3/2,0)+(0,3/2) matter fields, and the same conclusions obtained. Massless limit is discussed in detail. (Typos uncorrected, Part of the work published and extended in several journal articles, for an important correction see physics/9702005).

We discuss the status and some perspectives of relativistic quantum physics.

We discuss the status and some perspectives of relativistic quantum physics.

The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. Volume 1 of this updated edition provides a broad introduction to the first of these theories, QED. The book begins with self-contained presentations of relativistic quantum mechanics and electromagnetism as a gauge theory. Lorentz transformations, discrete symmetries, and Majorana fermions are covered. A unique feature is the elementary introduction to quantum field theory, leading in easy stages to covariant perturbation theory and Feynman graphs, thereby establishing a firm foundation for the formal and conceptual framework upon which the subsequent development of the three quantum gauge field theories of the Standard Model is based. Detailed tree-level calculations of physical processes in QED are presented, followed by an elementary treatment of one-loop renormalization of a model scalar field theory, and then by the realistic case of QED. The text includes updates on nucleon structure functions and the status of QED, in particular the precision tests provided by the anomalous magnetic moments of the electron and muon. The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight. Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an introduction to the Standard Model of particle physics. Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two. Anthony J.G. Hey is now Honorary Senior Data Scientist at the UK’s National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the ‘MPI’ message passing standard. After leaving Southampton in 2001 he was director of the UK’s ‘eScience’ initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.’s Rutherford Appleton Laboratory. He then founded a new ‘Scientific Machine Learning’ group to apply AI technologies to the ‘Big Scientific Data’ generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of ‘The Feynman Lectures on Computation’.

The fifth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of Higgs and top sector physics, as well as CP violation and neutrino oscillations. It offers an accessible and practical introduction to the three gauge theories comprising the Standard Model of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD), and the Glashow-Salam-Weinberg (GSW) electroweak theory. Volume 1 of this updated edition provides a broad introduction to the first of these theories, QED. The book begins with self-contained presentations of relativistic quantum mechanics and electromagnetism as a gauge theory. Lorentz transformations, discrete symmetries, and Majorana fermions are covered. A unique feature is the elementary introduction to quantum field theory, leading in easy stages to covariant perturbation theory and Feynman graphs, thereby establishing a firm foundation for the formal and conceptual framework upon which the subsequent development of the three quantum gauge field theories of the Standard Model is based. Detailed tree-level calculations of physical processes in QED are presented, followed by an elementary treatment of one-loop renormalization of a model scalar field theory, and then by the realistic case of QED. The text includes updates on nucleon structure functions and the status of QED, in particular the precision tests provided by the anomalous magnetic moments of the electron and muon. The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight. Each volume should serve as a valuable handbook for students and researchers in advanced particle physics looking for an introduction to the Standard Model of particle physics. Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two. Anthony J.G. Hey is now Honorary Senior Data Scientist at the UK’s National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the ‘MPI’ message passing standard. After leaving Southampton in 2001 he was director of the UK’s ‘eScience’ initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.’s Rutherford Appleton Laboratory. He then founded a new ‘Scientific Machine Learning’ group to apply AI technologies to the ‘Big Scientific Data’ generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of ‘The Feynman Lectures on Computation’.