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The onset and the development of the concept of exchange force in quantum physics are historically reconstructed, starting from Heisenberg's seminal contributions in 1926 and going through the great developments in nuclear physics, which allowed the emergence of the idea of force mediating virtual quanta. Although most of such work was performed in Europe, the last and decisive effort in this long path was carried out by Japanese scientists in the 1930s. This is the main focus of the present work, which retraces the achievements of Yukawa and Tomonaga, whose results and mutual interactions are carefully analyzed and related to those of European physicists., Comment: 37 pages, no figures, Springer Nature style, submitted for publication

The broad debate on foundational issues in quantum mechanics, which took place at the famous 1957 Chapel Hill conference on \textit{The Role of Gravitation in Physics}, is here critically analyzed with an emphasis on Richard Feynman's contributions. One of the most debated questions at Chapel Hill was whether the gravitational field had to be quantized and its possible role in wave function collapse. Feynman's arguments in favor of the quantization of the gravitational field, based essentially on a series of gedanken experiments, are here discussed. Then the related problem of the wave function collapse, for which Feynman hints to decoherence as a possible solution, is discussed. Finally, another topic is analyzed, concerning the role of the observer in a closed Universe. In this respect, Feynman's many-worlds characterization of Everett's approach at Chapel Hill is discussed, together with later contributions of his, including a kind of Schr\"{o}dinger's cat paradox, which are scattered throughout the 1962-63 Lectures on Gravitation. Philosophical implications of Feynman's ideas in relation to foundational issues are also discussed., Comment: 14 pages, no figures. Based on the talk given by AN at the 16th Marcel Grossmann Conference, parallel session HR3 (Time and Philosophy in Physics). arXiv admin note: substantial text overlap with arXiv:2102.11220

In this contribution we report about Feynman's approach to gravitation, starting from the records of his interventions at the Chapel Hill Conference of 1957. As well known, Feynman was concerned about the relation of gravitation with the rest of physics. Probably for this reason, he promoted an unusual, field theoretical approach to general relativity, in which, after the recognition that the interaction must be mediated by the quanta of a massless spin-$2$ field, Einstein's field equations should follow from the general properties of Lorentz-invariant quantum field theory, plus self-consistency requirements. Quantum corrections would then be included by considering loop diagrams. These ideas were further developed by Feynman in his famous lectures on gravitation, delivered at Caltech in 1962-63, and in a handful of published papers, where he also introduced some field theoretical tools which were soon recognized to be of general interest, such as ghosts and the tree theorem. Some original pieces of Feynman's work on gravity are also present in a set of unpublished lectures delivered at Hughes Aircraft Company in 1966-67 and devoted primarily to astrophysics and cosmology. Some comments on the relation between Feynman's approach to gravity and his ideas on the quantum foundations of the fundamental interactions are included., Comment: 13 pages, no figures. Based on the talk given by AN at the 16th Marcel Grossmann Conference, parallel session HR2 (History of Relativity, Gravitation and Cosmology). arXiv admin note: text overlap with arXiv:2102.11220

An account of Richard Feynman's work on gravitational waves is given. Feynman's involvement with this subject can be traced backto 1957, when he attended the famous Chapel Hill conference on the Role of Gravitation in Physics. At that conference, he presented in particular the celebrated sticky bead argument, which was devised to intuitively argue that gravitational waves must carry energy, if they exist at all. While giving a simple argument in favor of the existence of gravitational waves, Feynman's thought experiment paved the way for their detection and stimulated subsequent efforts in building a practical detecting device. Feynman's contributions were systematically developed in a letter to Victor Weisskopf, completed in February 1961, as well as in his Caltech Lectures on Gravitation, delivered in 1962-63. There, a detailed calculation of the power radiated as gravitational radiation was performed, using both classical and quantum field theoretical tools, leading to a derivation of the quadrupole formula and its application to gravitational radiation by a binary star system. A comparison between the attitudes of Feynman and of the general relativity community to the problems of gravitational wave physics is drawn as well., Comment: 20 pages, 1 figure. Based on the talk given by MD at the 16th Marcel Grossmann Conference, parallel session HR2 (History of Relativity, Gravitation and Cosmology)

Richard P. Feynman's work on gravitation, as can be inferred from several published and unpublished sources, is reviewed. Feynman was involved with this subject at least from late 1954 to the late 1960s, giving several pivotal contributions to it. Even though he published only three papers, much more material is available, beginning with the records of his many interventions at the Chapel Hill conference in 1957, which are here analyzed in detail, and show that he had already considerably developed his ideas on gravity. In addition he expressed deep thoughts about fundamental issues in quantum mechanics which were suggested by the problem of quantum gravity, such as superpositions of the wave functions of macroscopic objects and the role of the observer. Feynman also lectured on gravity several times. Besides the famous lectures given at Caltech in 1962-63, he extensively discussed this subject in a series of lectures delivered at the Hughes Aircraft Company in 1966-67, whose focus was on astronomy and astrophysics. All this material allows to reconstruct a detailed picture of Feynman's ideas on gravity and of their evolution until the late sixties. According to him, gravity, like electromagnetism, has quantum foundations, therefore general relativity has to be regarded as the classical limit of an underlying quantum theory; this quantum theory should be investigated by computing physical processes, as if they were experimentally accessible. The same attitude is shown with respect to gravitational waves, as is evident also from an unpublished letter addressed to Victor F. Weisskopf. In addition, an original approach to gravity, which closely mimics (and probably was inspired by) the derivation of the Maxwell equations given by Feynman in that period, is sketched in the unpublished Hughes lectures., Comment: 47 pages, no figures, final version. Dedicated to the Memory of Erasmo Recami

We retrace an ab initio relativistic derivation of Maxwell's equations that was developed by Feynman in unpublished notes, clarifying the analogies and the differences with analogous treatments present in the literature. Unlike the latter, Feynman's approach stands out because it considers electromagnetic potentials as primary, reflecting his ideas about the quantum foundations of electromagnetism. Some considerations about the foundations of special relativity, which are naturally suggested by this approach, are given in appendix., Comment: 17 pages, no figures, submitted for publication

We analyze Feynman's work on the response of an amplifier performed at Los Alamos and described in a technical report of 1946, as well as lectured on at the Cornell University in 1946-47 during his course on Mathematical Methods. The motivation for such a work was Feynman's involvement in the Manhattan Project, for which the necessity emerged of feeding the output pulses of counters into amplifiers or several other circuits, with the risk of introducing distortion at each step. In order to deal with such a problem, Feynman designed a theoretical "reference amplifier", thus enabling a characterization of the distortion by means of a benchmark relationship between phase and amplification for each frequency, and providing a standard tool for comparing the operation of real devices. A general theory was elaborated, from which he was able to deduce the basic features of an amplifier just from its response to a pulse or to a sine wave of definite frequency. Moreover, in order to apply such a theory to practical problems, a couple of remarkable examples were worked out, both for high-frequency cutoff amplifiers and for low-frequency ones. A special consideration deserves a mysteriously exceptional amplifier with best stability behavior introduced by Feynman, for which different physical interpretations are here envisaged. Feynman's earlier work then later flowed in the Hughes lectures on Mathematical Methods in Physics and Engineering of 1970-71, where he also remarked on causality properties of an amplifier, that is on certain relations between frequency and phase shift that a real amplifier has to satisfy in order not to allow output signals to appear before input ones. Quite interestingly, dispersion relations to be satisfied by the response function were introduced., Comment: 19 pages, 6 figures

We discuss a previously unpublished description of electromagnetism outlined by Richard P. Feynman in the 1960s in five handwritten pages, recently uncovered among his papers, and partly developed in later lectures. Though similar to the existing approaches deriving electromagnetism from special relativity, the present one extends a long way towards the derivation of Maxwell's equations with minimal physical assumptions. In particular, without postulating Coulomb's law, homogeneous Maxwell's equations are written down by following a route different from the standard one, i.e. first introducing electromagnetic potentials in order to write down a relativistic invariant action, which is just the inverse approach to the usual one. Also, Feynman's derivation of the Lorentz force exclusively follows from its linearity in the charge velocity and from relativistic invariance. Going further, i.e. adding the inhomogeneous Maxwell's equations, requires some more physical input, and can be done by just following conventional lines, hence this task was not pursued here. Despite its incompleteness, this way of proceeding is of great historical and epistemological significance. We also comment about its possible relevance to didactics, as an interesting supplement to usual treatments., Comment: 17 pages, no figures

We discuss a less known aspect of Feynman's multifaceted scientific work, centered about his interest in molecular biology, which came out around 1959 and lasted for several years. After a quick historical reconstruction about the birth of molecular biology, we focus on Feynman's work on genetics with Robert S. Edgar in the laboratory of Max Delbruck, which was later quoted by Francis Crick and others in relevant papers, as well as in Feynman's lectures given at the Hughes Aircraft Company on biology, organic chemistry and microbiology, whose notes taken by the attendee John Neer are available. An intriguing perspective comes out about one of the most interesting scientists of the XX century., Comment: On the centenary of the birth of Richard P. Feynman (May 11, 1918 - February 15, 1988)

The goal of international trade theories is to explain the exchange of goods and services between different countries, aiming to benefit from it. Albeit the idea is very simple and known since ancient history, smart policy and business strategies need to be implemented by each subject, resulting in a complex as well as not obvious interplay. In order to understand such a complexity, different theories have been developed since the sixteenth century and today new ideas still continue to enter the game. Among them, the so called classical theories are country-based and range from Absolute and Comparative Advantage theories by A. Smith and D. Ricardo to Factor Proportions theory by E. Heckscher and B. Ohlin. In this work we build a simple hydrodynamic model, able to reproduce the main conclusions of Comparative Advantage theory in its simplest setup, i.e. a two-country world with country A and country B exchanging two goods within a genuine exchange-based economy and a trade flow ruled only by market forces. The model is further generalized by introducing money in order to discuss its role in shaping trade patterns. Advantages and drawbacks of the model are also discussed together with perspectives for its improvement., Comment: 8 pages, 2 figures

Understanding consumption dynamics and its impact on the whole economy and welfare within the present economic crisis is not an easy task. Indeed the level of consumer demand for different goods varies with the prices, consumer incomes and demographic factors. Furthermore crisis may trigger different behaviors which result in distortions and amplification effects. In the present work we propose a simple model to quantitatively describe the time evolution over a brief period of the amount of money an average consumer decides to spend, depending on his/her available budget. A simple hydrodynamical analog of the model is discussed. Finally, perspectives of this work are briefly outlined., Comment: 5 pages, 7 figures

An important issue within the present economic crisis is understanding the dynamics of the public debt of a given country, and how the behavior of average consumers and tax payers in that country affects it. Starting from a model of the average consumer behavior introduced earlier by the authors, we propose a simple model to quantitatively address this issue. The model is then studied and analytically solved under some reasonable simplifying assumptions. In this way we obtain a condition under which the public debt steadily decreases., Comment: 4 pages, 1 figures, submitted for publication to Physica A

We study multi-soliton solutions of the four-dimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of $S^{2}$ into $CP^{N-1}$ and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric setup allows to introduce a parameter which is related to the 't Hooft coupling of a suitable large $N$ limit, in which $N\rightarrow\infty$ and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it., Comment: 29 pages, 7 figures, minor changes, matches published version

A possible mechanism for the spontaneous breaking of SUSY, based on the presence of vacuum condensates, is reviewed. Such a mechanism could occur in many physical examples, both at the fundamental and emergent level, and would be formally analogous to spontaneous SUSY breaking at finite temperature in the TFD formalism, in which case it can be applied as well. A possible experimental setup for detecting such a breaking through measurement of the Anandan-Aharonov invariants associated with vacuum condensates in an optical lattice model is proposed., Comment: 6 pages, 2 figures, review article to appear in the special issue "Supersymmetry, Supergravity, and Superstring Phenomenology" of Advances in High Energy Physics

In this work is presented a microbalance for single microparticle sensing based on resonating AFM cantilever. The variation of the resonator eigenfrequency is related to the particle mass positioned at the free apex of the cantilever. An all-digital phase locked loop (PLL) control system is developed to detect the variations in cantilever eigenfrequency. Two particle populations of different materials are used in the experimental test, demonstrating a mass sensitivity of 15 Hz/pg in ambient conditions. Thereby it is validated the possibility of developing an inexpensive, portable and sensitive microbalance for point-mass sensing., Comment: 5 pages, 4 figures

Spontaneous supersymmetry (SUSY) breaking is revealed in all phenomena in which vacuum condensates are physically relevant. The dynamical breakdown of SUSY is generated by the condensates themselves, which lift the zero point energy. Evidence is presented in the case of the Wess-Zuimino model, and the flavor mixing case is treated in detail., Comment: 5 pages

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon an ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial r\^{o}le in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess--Zumino model, that can be considered an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice., Comment: 5 pages

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two Wess--Zumino $\mathcal{N}=1$ supermultiplets and arguments for its general validity are given. The mechanism relies on the fact that, despite mixing treats fermions and bosons symmetrically, both the fermionic and the bosonic zero point energies are shifted by a positive amount and this kind of shift does not respect supersymmetry., Comment: 5 pages, 1 figure, Eq(12) of V1 corrected to Eq(22), explicit off-shell formulation included, one reference added

We discuss the existence of a non-abelian gauge structure associated with flavor mixing. In the specific case of two flavor mixing of Dirac neutrino fields, we show that this reformulation allows to define flavor neutrino states which preserve the Poincar\'e structure. Phenomenological consequences of our analysis are explored., Comment: 13 pages, 2 figures