On some equations concerning quantum electrodynamics coupled to quantum gravity, the gravitational contributions to the gauge couplings and quantum effects in the theory of gravitation: mathematical connections with some sector of String Theory and Number Theory

This paper is principally a review, a thesis, of principal results obtained from various authoritative theoretical physicists and mathematicians in some sectors of theoretical physics and mathematics. In this paper in the Section 1, we have described some equations concerning the quantum electrodynamics coupled to quantum gravity. In the Section 2, we have described some equations concerning the gravitational contributions to the running of gauge couplings. In the Section 3, we have described some equations concerning some quantum effects in the theory of gravitation. In the Section 4, we have described some equations concerning the supersymmetric Yang-Mills theory applied in string theory and some lemmas and equations concerning various gauge fields in any non-trivial quantum field theory for the pure Yang-Mills Lagrangian. Furthermore, in conclusion, in the Section 5, we have described various possible mathematical connections between the argument above mentioned and some sectors of Number Theory and String Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings

On the possible mathematical connections between the Hartle-Hawking no boundary proposal concerning the Randall-Sundrum cosmological scenario, Hartle-Hawking wave-function in the mini-superspace sector of physical superstring theory, p-adic Hartle-Hawking wave function and some sectors of Number Theory.

In this paper we have described the Hartle-Hawking no boundary proposal concerning the Randall-Sundrum cosmological scenario, nonlocal braneworld action in the two-brane Randall-Sundrum model, Hartle-Hawking wave-function in the mini-superspace sector of physical superstring theory, p-adic models in the Hartle-Hawking proposal and p-adic and adelic wave functions of the universe. Furthermore, we have showed some possible mathematical connections between some equations of these arguments and, in conclusion, we have also described some mathematical connections between some equations of arguments above mentioned and some equations concerning the Riemann zeta function, the Ramanujan’s modular equations and the Palumbo-Nardelli model. In the section 1, we have described the Hartle-Hawking “no boundary” proposal applied to Randall-Sundrum cosmological scenario. In the section 2, we have described nonlocal braneworld action in the two-brane Randall-Sundrum model. In the section 3, we have described the compactifications of type IIB strings on a Calabi-Yau three-fold and Hartle-Hawking wave-function in the mini-superspace sector of physical superstring theory. In the section 4, we have described the p-Adic models in the Hartle-Hawking proposal. In the section 5, we have described the p-Adic and Adelic wave functions of the Universe. In the section 6, we have described some equations concerning the Riemann zeta function, specifically, the Goldston-Montgomery Theorem, the study of the behaviour of the argument of the Riemann function with the condition that s lies on the critical line s=1/2+it, where t is real, the P-N Model (Palumbo-Nardelli model) and the Ramanujan identities. In conclusion, in the section 7, we have described some possible mathematical connections between some equations of arguments above discussed and some equations concerning the Riemann zeta-function, the Ramanujan’s modular equations and the Palumbo-Nardelli model

Zero Modes and Conformal Anomaly in Liouville Vortices

The partition function of a two dimensional Abelian gauge model reproducing magnetic vortices is discussed in the harmonic approximation. Classical solutions exhibit conformal invariance, that is broken by statistical fluctuations, apart from an exceptional case. The corresponding ``anomaly'' has been evaluated. Zero modes of the thermal fluctuation operator have been carefully discussed.Comment: RevTex, 14 pages, no figures. To appear on Nucl. Phys.

Topology of Networks in Generalized Musical Spaces

The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this foundation, I generalize the concept of musical spaces as networks and derive functional principles of compositional design by the direct analysis of the network topology. This approach provides a novel framework for the analysis and quantification of similarity of musical objects and structures, and suggests a way to relate such measures to the human perception of different musical entities. Finally, the analysis of a single work or a corpus of compositions as complex networks provides alternative ways of interpreting the compositional process of a composer by quantifying emergent behaviors with well-established statistical mechanics techniques. Interpreting the latter as probabilistic randomness in the network, I develop novel compositional design frameworks that are central to my own artistic research

Quantum field theory with varying couplings

A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific choice of the coupling's profile for any finite-order perturbative expansion. For one of these cases, some tree and one-loop diagrams are calculated. This is an example of a theory where violation of Lorentz symmetry is not enhanced at the quantum level. We draw some consequences for the renormalization properties of certain classes of fractional field theories.Comment: 12 pages. v2: discussion improved, minor typos correcte

Heat kernel for Newton-Cartan trace anomalies

We compute the leading part of the trace anomaly for a free non-relativistic scalar in 2+1 dimensions coupled to a background Newton-Cartan metric. The anomaly is proportional to 1/m, where m is the mass of the scalar. We comment on the implications of a conjectured a-theorem for non-relativistic theories with boost invariance.Comment: 18 page

1+1 Dimensional Yang-Mills Theories in Light-Cone Gauge

In 1+1 dimensions two different formulations exist of SU(N) Yang Mills theories in light-cone gauge; only one of them gives results which comply with the ones obtained in Feynman gauge. Moreover the theory, when considered in 1+(D-1) dimensions, looks discontinuous in the limit D=2. All those features are proven in Wilson loop calculations as well as in the study of the $q\bar q$ bound state integral equation in the large N limit.Comment: Invited report at the Workshop "Low Dimensional Field Theory", Telluride (CO), Aug. 5-17 1996; 16 pages, latex, no figures To appear in International Journal of Modern Physics A minor misprints correcte

On a Model for Integrated Information

In this paper we give a thorough presentation of a model proposed by Tononi et al. for modeling \emph{integrated information}, i.e. how much information is generated in a system transitioning from one state to the next one by the causal interaction of its parts and \emph{above and beyond} the information given by the sum of its parts. We also provides a more general formulation of such a model, independent from the time chosen for the analysis and from the uniformity of the probability distribution at the initial time instant. Finally, we prove that integrated information is null for disconnected systems

Probability of informed trading: an empirical application to the euro overnight market rate.

This paper presents a microstructure model for the unsecured overnight euro money market, similar to that developed for stock markets by Easley and O'Hara (1992). More specifically, this paper studies the role of heterogeneity in the population of banks participating on this market, and the influence of the institutional framework and market organizational aspects of the overnight deposit market. A first empirical assessment of the functioning of this market is based on the probability of informed trade which measures the ability of traders (banks) to interpret signals on the expected evolution of the overnight rate. This indicator is estimated on real-time data publicly available to market participants. Results show that between 2000 and 2004 a heterogeneous learning process of market mechanisms within participants could be observed. From 2005 onwards, however, heterogeneity in the learning process sharply decreased. Moreover, the empirical evidence show that the March 2004 changes in Eurosystem's operational framework have modified the informational patterns of order flow in the euro area money market: informed trades became even more predominant between the last main refinancing operation and the end of the reserves maintenance period than they were before March 2004.Euro overnight market ; PIN models ; Microstructure, Monetary policy.