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Quantum field theory was established about a hundred years ago and is the result of combining the principles of quantum mechanics and the special theory of relativity. Historically, some of the founding fathers were at high unease as intermediate calculations led to infinities. A different approach, sometimes called the analytic S-matrix or the bootstrap, relying on basic principles such as causality and unitarity, was put forward. A resurgence of these fields has taken place now since their power has not been tapped to the fullest, and are the most active fields of research in theoretical physics and spurring developments in computer algebra. In this article, after recalling the history of this field, we highlight some of the past and recent contributions from India. [ABSTRACT FROM AUTHOR]

The notion of cumulative activity for elastic events in hadron collision is introduced. The interrelation between centrality and cumulative activities of the elastic and inelastic events has been established for hadron scattering. Considerations on its application are presented. [ABSTRACT FROM AUTHOR]

You might have heard about various mathematical properties of scattering amplitudes such as analyticity, sheets, branch cuts, discontinuities, etc. What does it all mean? In these lectures, we will take a guided tour through simple scattering problems that will allow us to directly trace such properties back to physics. We will learn how different analytic features of the S-matrix are really consequences of causality, locality of interactions, unitary propagation, and so on. These notes are based on a series of lectures given in Spring 2023 at the Institute for Advanced Study in Princeton and the Higgs Centre School of Theoretical Physics in Edinburgh. [ABSTRACT FROM AUTHOR]

Divergences that occur in density matrices of decay and scattering processes are shown to be regularized by tracing and unitarity or the optical theorem. These divergences are regularized by the lifetime of the decaying particle or the total scattering cross section. Also, these regularizations are shown to give the expected helicities of final particles. As an illustration, the density matrix is derived for the weak decay of a polarized muon at rest, µ- → νµ(e-ν¯e), with Lorentz invariant density matrix entries and unitarity upheld at tree level. The electron’s von Neumann entanglement entropy distributions are derived with respect to both the electron’s emission angle and energy. The angular entropy distribution peaks for an electron emitted backward with respect to the muon’s polarization given a minimum volume regularization larger than the cube of the muon’s Compton wavelength. The kinematic entropy distribution is maximal at half the muon’s rest mass energy. These results are similar to the electron’s angular and kinematic decay rate distributions. Both the density matrix and entanglement entropy can be cast in terms of either ratios of areas or volumes.

Unitarity and the optical theorem are used to derive the reduced density matrices of Compton scattering in the presence of a witness particle. Two photons are initially entangled wherein one photon participates in Compton scattering, while the other is a witness, i.e., does not interact with the electron. Unitarity is shown to require that the entanglement entropy of the witness photon does not change after its entangled partner undergoes scattering. The final mutual information of the electron's and witness particle's polarizations is shown to be nonzero for low-energy Compton scattering. This indicates that the two particles became correlated in spite of no direct interaction. Assuming an initial maximally entangled state, the change in entanglement entropy of the scattered photon's polarization is calculated in terms of Stokes parameters. A common ratio of areas occurs in the final reduced density matrix elements, von Neumann entropies, Stokes parameter, and mutual information. This common ratio consists of the Thomson scattering cross-section and an accessible regularized scattering area. [ABSTRACT FROM AUTHOR]

We introduce the notion of cumulative activity for inelastic events generated under hadron collisions, and discuss its energy dependence and connection with the reflective scattering mode. These issues are relevant for enlightening the asymptotic dynamics in view of the LHC measurements. [ABSTRACT FROM AUTHOR]

The transition from the weakly interacting BCS regime to the strongly interacting unitary regime is explored for ultracold trapped Fermi gases assuming a normal mode description of the gas instead of the conventional Cooper pairing. The Pauli principle is applied "on paper" using specific normal mode assignments. Energies, entropies, critical temperatures, and an excitation frequency are studied and compared with existing results in the literature. These normal modes have been derived analytically for N identical, confined particles from a first-order L = 0 group theoretic solution of a three-dimensional Hamiltonian with a general two-body interaction. In previous studies, normal modes were able to describe the unitary regime obtaining ground-state energies comparable to benchmark results and thermodynamic quantities in excellent agreement with experiment. As a precurser to this work, the behavior of the normal mode frequencies was investigated across the BCS to unitarity transition, and a microscopic basis of the large excitation gaps and universal behavior at unitarity was proposed. The current study now explores the ability of these normal mode frequencies to determine various properties along this transition, testing the ability of the microscopic dynamics of these normal modes to produce observable behavior away from unitarity. The results suggest that the physics of superfluidity can be described using normal modes across a wide range of interparticle interaction strengths and thus offers a clear microscopic alternative to the two-body pairing models commonly used to describe superfluidity along this transition. [ABSTRACT FROM AUTHOR]

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In this study, we consider the symmetry property of the inelastic overlap function and its relation to the reflective scattering mode appearance. This symmetry property disfavors an exclusion of one of the scattering modes—the reflective mode—when approaching the asymptotic limit. Predominance of the particular mode correlates with the energy and impact parameters ranges.

We introduce the notion of reflective ability and discuss its energy dependence using rational form of unitarization. Correspondence with the phase of exponential unitarization is traced. Increase of the reflective ability of interaction region starts at the LHC energies. Numerical estimates are given. [ABSTRACT FROM AUTHOR]

In this study, we consider the symmetry property of the inelastic overlap function and its relation to the reflective scattering mode appearance. This symmetry property disfavors an exclusion of one of the scattering modes—the reflective mode—when approaching the asymptotic limit. Predominance of the particular mode correlates with the energy and impact parameters ranges. [ABSTRACT FROM AUTHOR]

We suggest a new explanation of the flatness of galaxies rotation curves without invoking dark matter. For this purpose, a new gravitational tensor field is introduced in addition to the metric tensor. [ABSTRACT FROM AUTHOR]

We consider two possible options of the energy dependency of the elastic and inelastic overlap functions. Those correspond to saturation of the black disk limit (BEL effect) and to the unitarity saturation (REL effect) at s â†' ∞. Relation of the REL effect to increase of the ratio σ el(s)/ σ tot(s) and emergence of black ring picture at the LHC is underlined. [ABSTRACT FROM AUTHOR]

Quantum decoherence is crucial to understanding the emergence of the classical world from the underlying quantum reality. Decoherence dynamics are unitary, although they superselect a preferred eigenbasis. Decoherence dynamics result in stable macroscopic, localized, classical-like states. We show that the above-mentioned facts imply the possibility of the existence of decoherence-like dynamics that result in stable macroscopic non-localized non-classical-like states. Being rooted in the fabric of the decoherence theory itself, this property implies environments that steer the decoherence towards, for example, spatial superpositions of macroscopic objects. To demonstrate this, we provide thought-experimental, mathematical and philosophical arguments. [ABSTRACT FROM AUTHOR]

Here, we explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at finite time implies quantum singularity resolution, but for a clock that encounters future infinity at finite time leads to a quantum recollapse. We then find that our starting point — assuming the general covariance of general relativity — is actually incompatible with general quantum unitarity: singularity resolution in quantum gravity can always be engineered by choosing the right clock, or avoided by using a different one. [ABSTRACT FROM AUTHOR]

A systematic procedure is proposed for better understanding the evolution laws of black holes in terms of pure quantum states. We start with the two opposed regions I and I I in the Penrose diagram, and study the evolution of matter in these regions, using the algebra derived earlier from the Shapiro effect in quantum particles. Since this spacetime has two distinct asymptotic regions, one must assume that there is a mechanism that reduces the number of states. In earlier work we proposed that region I I describes the angular antipodes of region I, the 'antipodal identification', but this eventually leads to contradictions. Our much simpler proposal is now that all states defined in region I I are exact quantum clones of those in region I. This indicates more precisely how to restore unitarity by making all quantum states observable, and in addition suggests that generalisations towards other black hole structures will be possible. An apparent complication is that the wave function must evolve with a purely antisymmetric, imaginary-valued Hamiltonian, but this complication can be well-understood in a realistic interpretation of quantum mechanics. [ABSTRACT FROM AUTHOR]

We provide arguments for the use of the rational form of unitarization, its relation with the diffraction peak shrinkage and asymptotics of the inelastic cross-section. The particular problems of the Regge model and the exponential form of unitarization with a factorized eikonal are discussed as well. A central role belongs to the asymptotic amplitude factorization resulting from Mandelstam analyticity and its symmetry over the scattering variables. [ABSTRACT FROM AUTHOR]

The LHC data on the elastic scattering indicate that the forward slope increase is not consistent with the contributions of the simple Regge poles only with the linear Regge trajectories. The dynamics might be associated with unitarization in the direct channel of reaction. We discuss the problems of the Regge model and provide a respective illustration of the direct-channel option.

We analyze the R + R² model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a selfconsistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters. [ABSTRACT FROM AUTHOR]

This essay contends that in quantum gravity, some spatial regions do not admit a unitary Hilbert space. Because the gravitational path integral spontaneously breaks CPT symmetry, "states" with negative probability can be identified on either side of trapped surfaces. I argue that these negative norm states are tolerable, by analogy to quantum mechanics. This viewpoint suggests a resolution of the firewall paradox, similar to black hole complementarity. Implications for cosmology are briefly discussed. [ABSTRACT FROM AUTHOR]

We suggest a new explanation of the flatness of galaxies rotation curves without invoking dark matter. For this purpose, a new gravitational tensor field is introduced in addition to the metric tensor.

Quantum decoherence is crucial to understanding the emergence of the classical world from the underlying quantum reality. Decoherence dynamics are unitary, although they superselect a preferred eigenbasis. Decoherence dynamics result in stable macroscopic, localized, classical-like states. We show that the above-mentioned facts imply the possibility of the existence of decoherence-like dynamics that result in stable macroscopic non-localized non-classical-like states. Being rooted in the fabric of the decoherence theory itself, this property implies environments that steer the decoherence towards, for example, spatial superpositions of macroscopic objects. To demonstrate this, we provide thought-experimental, mathematical and philosophical arguments.

Some classical aspects of Metric–Affine Gravity are reviewed in the context of the F (n) (R) type models (polynomials of degree n in the Riemann tensor) and the topologically massive gravity. At the nonperturbative level, we explore the consistency of the field equations when the F (n) (R) models are reduced to a Riemann–Christoffel (RCh) space–time, either via a Riemann–Cartan (RC) space or via an Einstein–Weyl (EW) space. It is well known for the case F (1) (R) = R that any path or reduction "classes" via RC or EW leads to the same field equations with the exception of the F (n) (R) theories for n > 1. We verify that this discrepancy can be solved by imposing nonmetricity and torsion constraints. In particular, we explore the case F (2) (R) for the interest in expected physical solutions as those of conformally flat class. On the other hand, the symmetries of the topologically massive gravity are reviewed, as the physical content in RC and EW scenarios. The appearance of a nonlinearly modified selfdual model in RC and existence of many nonunitary degrees of freedom in EW with the suggestion of a modified model for a massive gravity which cure the unphysical propagations shall be discussed. [ABSTRACT FROM AUTHOR]

We perform a comprehensive study of the Higgs potential of the two Higgs doublet model extended by a real triplet scalar field Δ. This model, dubbed 2 HDM + T , has a rich Higgs spectrum consisting of three CP-even Higgs h 1 , 2 , 3 , one CP-odd A 0 and two pairs of charged Higgs H 1 , 2 ± . First, we determine the perturbative unitarity constraints and a set of nontrivial conditions for the boundedness from below (BFB). Then we derive the Veltman conditions by considering the quadratic divergencies of Higgs boson self-energies in 2 HDM + T. We find that the parameter space is severely delimited by these theoretical constraints, as well as experimental exclusion limits and Higgs signal rate measurements at LEP and LHC. Using HiggsBounds-5.3.2beta and HiggSignals-2.2.3beta public codes, an exclusion test at 2 σ is then performed on the physical scalars of 2 HDM + T. Our analysis provides a clear insight on the nonstandard scalar masses, showing that the allowed ranges are strongly sensitive to the sign of mixing angle α 1 , essentially when naturalness is involved. For α 1 < 0 scenario, our results place higher limits on the bounds of all scalar masses, and show that the pairs (h 2 , H 1 ±) and (h 3 , H 2 ±) are nearly mass degenerate varying within the intervals [ 1 3 0 , 2 4 6 ] GeV and [ 1 6 0 , 3 3 5 ] GeV, respectively. When α 1 turns positive, we show that consistency with theoretical constraints and current LHC data, essentially on the diphoton decay channel, favors Higgs masses varying within wide allowed ranges: [ 1 5 3 , 9 7 3 ] GeV for m A 0 ; [ 1 5 1 , 9 2 8 ] GeV for ( m h 2 , m H 1 ± ) and [ 1 8 6 , 9 7 9 ] GeV for ( m h 3 , m H 2 ± ). Finally, we find that the γ γ and Z γ Higgs decay modes are generally correlated if tan β lies within the reduced intervals 1 7 ≤ tan β ≤ 2 5 and λ b parameter is frozen around 1. 3 (1. 1) for sin α 1 > 0 (sin α 1 < 0). [ABSTRACT FROM AUTHOR]

Aim. The article aims to investigate the essential and content characteristics of unitarism as a phenomenon of contemporary constitutional law. The synergistic connection between the doctrine of modern unitarism, the principles of unitarity of the state territory and the fundamental institutions of political-legal and state-administrative life of modern unitary states is shown. It proves that the unitary system is not only one of the important components of the process of accomplishing the tasks, goals and functions of most modern states, but also an immanent feature and strategic element of the mechanism of exercising their sovereign rights. Methods. The methodological basis encompasses philosophico-ideological, general scientific principles and approaches and special scientific methods of inquiry for constitutional and legal phenomena and processes. The philosophico-ideological basis of the study is the position of dialectics, on the basis of which the causes and factors of the evolution of unitarism are thoroughly investigated. In general, the research was conducted on the basis of a combination of ontological, epistemological and axiological analysis of contemporary unitarism. Results. The complexity, importance and relatively widespread use of unitarity as a form of government is causing a lively and ever-growing scientific interest in it throughout the world. The unique capability of unitarism to take into account the specific features of a particular condition allows it to manifest itself in each case in a new way. That is why it is important to analyze the mutual influence of unitary theory and practice, to explore and take into account the peculiarities of national unitarism. The problem of unitarism and the unitary form of the territorial structure of the state and the status of its constituents is one of the least studied in domestic constitutional law. Modern scholars studying constitutional law, as a rule, are limited to consideration of individual issues of the territory, in particular, the features of the territorial organization of state power and local self-government, problems of state sovereignty, territorial integrity and inviolability, etc. To a large extent, the problem has not been studied exhaustively in contemporary Ukraine which causes difficulties in understanding such interrelated but not identical phenomena as unitarism and unitarity, regionalism and regionalization, municipalism and municipalization, decentralization and deconcentration, etc. It should be noted that in modern literature related to problems of state territory, territorial organization of state power, and other issues of the status of territory, the complex, multidimensional nature of unitarism, as a constitutional category, is not always taken into account. Conclusions. Unitarism is proved to be a multidimensional socio-political and constitutional phenomenon: it is an idea, a theory, a scientific direction as well as a global social constitutional practice and a constitutional form of the existence and functioning of territorial communities, it is the historical condition of national statehood and Ukrainian regional civilization and the form of realization of the national identity and civic consciousness, etc.

We comment on phase selection of the scattering amplitude, emphasizing that the elastic overlap function should have a central impact parameter profile at high energies and highlighting the role of the reflective scattering mode at the LHC energies. Emerging problems with the use of peripheral impact parameter dependence of the elastic overlap function are explicitly indicated. Their solution is an elimination of the phases connected to peripheral form of the elastic overlap function. Contrary, we adhere to a relative peripheral form of the inelastic overlap function with an additional new feature of a maximum at nonzero value of the impact parameter at the highest energies. Phenomenologically, the dynamics of hadron scattering is motivated by a hadron structure with a hard central core presence.

We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into clusters, if mixed-symmetry of its wave function is enforced. We claim that any theory in which the two-body scattering length is much larger than any other scale involved exhibits such instability. We exemplify this with the inability of the leading-order pionless effective field theory to describe stable states of A>4 nuclei. A finite interaction range is identified as a sufficient condition for a bound mixed-symmetry system. The minimal value of this range depends on the proximity of a system to unitarity, on the number of constituents, and on the particular realization of discrete scale invariance of the three-body spectrum.

In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any effective smooth field theoretical description would miss part of the fundamental degrees of freedom and thus break unitarity. This is applicable also to trivial gravitational field (low energy) idealizations realized by the use of Minkowski background geometry which, as with any other spacetime geometry, corresponds, in the fundamental description, to infinitely many different and closely degenerate discrete microstates. The existence of such microstates provides a large reservoir q-bit for information to be coded at the end of black hole evaporation and thus opens the way to a natural resolution of the black hole evaporation information puzzle. In this paper we show that these expectations can be made precise in a simple quantum gravity model for cosmology motivated by loop quantum gravity. Concretely, even when the model is fundamentally unitary, when microscopic degrees of freedom irrelevant to low-energy cosmological observers are suitably ignored, pure states in the effective description evolve into mixed states due to decoherence with the Planckian microscopic structure. Moreover, in the relevant physical regime these hidden degrees of freedom do not carry any “energy” and thus realize, in a fully quantum gravitational context, the idea (emphasized before by Unruh and Wald) that decoherence can take place without dissipation, now in a concrete gravitational model strongly motivated by quantum gravity. All this strengthens the perspective of a quite conservative and natural resolution of the black hole evaporation puzzle where information is not destroyed but simply degraded (made unavailable to low-energy observers) into correlations with the microscopic structure of the quantum geometry at the Planck scale.

Nonlinear electrodynamics with two parameters is studied. It is shown that singularities of point-like electric charges are absent and the electromagnetic energy is finite. Corrections to Coulomb's law are found. The finite static electric field energy of a point-like charge is calculated. We demonstrate that the electron mass may have the electromagnetic nature. It was shown that principles of causality and unitarity take place. • Singularities of point-like electric charges are absent. • The electromagnetic energy is finite. • There are corrections to Coulomb's law. • The electron mass may have the electromagnetic nature. • Principles of causality and unitarity take place. [ABSTRACT FROM AUTHOR]

We provide arguments for the use of the rational form of unitarization, its relation with the diffraction peak shrinkage and asymptotics of the inelastic cross-section. The particular problems of the Regge model and the exponential form of unitarization with a factorized eikonal are discussed as well. A central role belongs to the asymptotic amplitude factorization resulting from Mandelstam analyticity and its symmetry over the scattering variables.