Monopoles, Clarified

Global constraints of Gauss' law and the solution to the strong CP problem

This chapter considers the role of the fundamental principles of quantum theory and principle thinking in quantum field theory, beginning with quantum electrodynamics. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory. Dirac’s work, in particular his derivation of his relativistic equation of the electron by combining the principles of relativity and quantum theory, is the main focus of this chapter, in parallel with Heisenberg’s work as the main focus in the discussion of quantum mechanics in Chap. 2. Heisenberg’s work, especially his paper introducing quantum mechanics, which Dirac studied very carefully, was a major influence on Dirac’s thinking throughout, I would argue, all of his work. This influence, however, does not diminish the originality and creativity of Dirac’s thinking, which, ultimately, led him to the discovery of his equation for the relativistic electron and antimatter, one of the greatest discoveries of fundamental physics. After a general introduction given in Sect. 6.1, Sect. 6.2 addresses Dirac’s discovery of his equation. It argues, along the lines of the argument developed in Chap. 2 in considering Heisenberg’s work, that Dirac’s discovery was that of a mathematical machinery, technology, responding to and, in some key respects, specifically as concerns the role of antimatter, anticipating the architecture of high-energy quantum phenomena, as manifested in the experimental technology that defines them. Although not a quantum field theory or even quite quantum electrodynamics, Dirac’s theory of the electron, based in his equation, provided some of the key physical, mathematical, and epistemological ingredients of quantum electrodynamics or quantum field theory as a viable nonrealist theory, to be considered here in terms of a particular concept of quantum field. Dirac’s equation, which expressly considered electrons as particles, was not a field equation, but given its essentially quantum-field-theoretical nature, it would also be difficult to see it merely in terms of relativistic quantum mechanics of particles, as some suggest. Sec. 6.3 addresses the architecture of quantum field theory, as grounded, in addition to the QD and QP/QS principles, which are, just as in quantum mechanics, primary, in the combination of the RWR principle and the particle-transformation, PT, principle. The PT principle emerged as a result of Dirac’s discovery of antimatter, an unintended consequence of his equation. New concepts of both “elementary particle” and “quantum field” are, I argue, required by the combination of both principles, and I shall suggest such concepts here. These concepts allow one to pose and relate the questions “What is a quantum field?” and “What is an elementary particle?” in a new way, even if not answer them. Sec. 6.4 discusses the role of renormalization, and comments on the future of quantum theory and fundamental physics given the current state of quantum field theory.

Magnetic monopoles as a new solution to strong CP problem

We show that in O'Raifeartaigh models of spontaneous supersymmetry breaking, R-symmetries can be broken by non-zero values of fields at tree level, rather than by vacuum expectation values of pseudomoduli at loop level. As a complement of the recent result by Shih, we show that there must be a field in the theory with R-charge different from zero and two in order for R-symmetry breaking to occur, no matter whether the breaking happens at tree or loop level. We review the example by CDFM, and construct two types of tree level R-symmetry breaking models with a wide range of parameters and free of runaway problem. And the R-symmetry is broken everywhere on the pseudomoduli space in these models. This provides a rich set of candidates for SUSY model building and phenomenology.

Dual conformal symmetry has had a huge impact on our understanding of planar scattering amplitudes in super Yang–Mills. At tree level, it combines with the original conformal symmetry generators to a Yangian algebra, a hallmark of integrability, and helps in determining the tree-level amplitudes. The latter are now known in closed form. At loop level, it determines the functional form of the four- and five-point scattering amplitudes to all orders in the coupling constant and gives restrictions at six points and beyond. The symmetry is best understood at loop level in terms of a novel AdS-inspired infrared regularization which makes the symmetry exact, despite the infrared divergences. This has important consequences for the basis of loop integrals in this theory. Recently, a number of selective reviews have appeared which discuss dual conformal symmetry, mostly at tree level. Here, we give an up-to-date account of dual conformal symmetry, focussing on its status at loop level.

When magnetic monopoles are assumed to exist in plasma dynamics, the propagation of electromagnetic waves is modified as Maxwell equations acquire a symmetrical structure due to the existence of electric and magnetic charge and current densities. This work presents a theoretical exploration on how far we can push the limits of a plasma theory under the presence of magnetic monopoles. In particular, we study the modification of ponderomotive forces in a plasma composed by electric and magnetic charges. We show that the general ponderomotive force on this plasma depends non-trivially on the magnetic monopoles, through the slow temporal and spatial variations of the electromagnetic field amplitudes. The magnetic charges introduce corrections even if the plasma is unmagnetized. Also, it is shown that the magnetic monopoles also experience a ponderomotive force due to the electrons. This force is in the direction of propagation of the electromagnetic waves.

The purpose of this research review is to examine the connection between the Schrödinger equation and quantum field theory. The method used in this review is a literature review of existing research on the topic. The results of the review indicate that the Schrödinger equation, which is a fundamental equation in quantum mechanics, can be derived from the principles of quantum field theory. This connection highlights the underlying unity of the two theories and helps to further our understanding of the behavior of subatomic particles. Additionally, it has been found that the Schrödinger equation is useful in describing the behavior of systems with a small number of particles, while quantum field theory is more appropriate for systems with a large number of particles. Research in this area has led to the development of new methods for solving the equation, such as the path integral approach, which provides a powerful tool for studying quantum systems with a large number of degrees of freedom. Additionally, the Schrödinger equation has led to the discovery of new symmetries and conservation laws, such as the AdS/CFT correspondence, which connects quantum field theory in anti-de Sitter space with a conformal field theory on the boundary of that space. Theoretical frameworks such as quantum field theory in curved spacetime and the holographic principle have also been developed to unify quantum mechanics and general relativity, and to understand the thermodynamic behavior of quantum systems and their behavior in extreme conditions. The study of quantum systems in non-equilibrium conditions is an active area of research and continues to yield new insights and discoveries. Overall, the research reviewed in this study suggests that the Schrödinger equation and quantum field theory are closely related, and that a deeper understanding of one can lead to a deeper understanding of the other. KEYWORDS: Schrödinger equation, quantum field theory, general relativity, quantum systems

We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We consider self-interacting scalars of general mass, but focus especially on the massless and conformally coupled cases. We show that certain contributions grow logarithmically in conformal time both at tree and loop level. We also consider gauge fields and gravitons. The four-dimensional Fefferman-Graham expansion of classical asymptotically de Sitter solutions is used to show that the wavefunction contains no logarithmic growth in the pure graviton sector at tree level. Finally, assuming a holographic relation between the wavefunction and the partition function of a conformal field theory, we interpret the logarithmic growths in the language of conformal field theory.

We propose a new path integral for QED in the presence of magnetic monopoles on the formalism of Geometric Algebra of Hestenes–Haddamard written in terms of Dirac matrices.

The resonant character of magnetic field damping by moving magnetic monopoles allows the field to survive indefinitely when the monopole plasma frequency is sufficiently large, even if the field is immersed in a conducting plasma. Dynamo growth of galactic field can still occur on time scales \ensuremath{\sim}${10}^{7}$-${10}^{8}$ yr in the presence of a halo composed of monopoles. A linear stability analysis suggests that a monopole's mass is $m\ensuremath{\sim}{10}^{18}$ GeV/${\mathit{c}}^{2}$ and that the monopoles should have an anisotropic flux \ensuremath{\sim}1 ${\mathrm{m}}^{\ensuremath{-}2}$ ${\mathrm{yr}}^{\ensuremath{-}1}$ ${\mathrm{sr}}^{\ensuremath{-}1}$.

We deal with the presence of magnetic monopoles in a non Abelian model that generalizes the standard 't~Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions which is called small monopole, since it is significantly smaller than the standard 't~Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole can be smaller or larger than the standard monopole, depending on the value of the parameter that controls the magnetic permeability of the model.

The so-called Witten effect implies a close relationship between the axion and magnetic monopole. A sound quantization in the presence of magnetic monopoles, called quantum electromagnetodynamics (QEMD), was utilized to construct a more generic axion-photon Lagrangian in the low-energy axion effective field theory. This generic axion-photon Lagrangian introduces the interactions between axion and two four-potentials, and leads to new axion-modified Maxwell equations. The interface haloscopes place an interface between two electromagnetic media with different properties and are desirable to search for high-mass axions ma≳O(10) μeV. In this work, for the generic axion-photon couplings built under QEMD, we perform comprehensive calculations of the axion-induced propagating waves and energy flux densities in different interface setups. We also obtain the sensitivity to new axion-photon couplings for high-mass axions. Published by the American Physical Society 2024

The validity of Poynting's theorem and the various expressions for the energy density, linear and angular momentum densities of the electromagnetic fields are re-examined in the presence of magnetic monopoles. It is found that the well known results in conventional electrodynamics without monopoles remain largely intact, provided that both the Maxwell equations and the Lorentz force law are modified in a consistent fashion as is already done previously in the literature.

We show that if we consider the full statement of Faraday's lawfor a closed physical circuit, the standard Maxwell's equationsin the presence of electric and magnetic charges have to includein their integral form a mixed term of the formρmve⊥, where ρm is the magnetic chargedensity and ve⊥ the perpendicular component of thevelocity ve of the electric charge.

Landauer's principle has seen a boom of interest in the last few years due to the growing interest in quantum information sciences. However, its relevance and validity in the contexts of quantum field theory (QFT) remain surprisingly unexplored. In the present paper, we consider Landauer's principle in qubit-cavity QFT interaction perturbatively, in which the initial state of the cavity QFT is chosen to be a vacuum or thermal state. In the vacuum case, the QFT always absorbs heat and jumps to excited states. For the qubit at rest, its entropy decreases, whereas if the qubit accelerates, it may also gain energy and it increases its entropy due to the Unruh effect. For the thermal state, the QFT can both absorb and release heat, depending on its temperature and the initial state of the qubit, and the higher-order perturbations can excite or deexcite the initial state to a higher or lower state. Landauer's principle is valid in all the cases we consider. We hope that this paper will pave the way for future explorations of Landauer's principle in QFT and gravity theories.