Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2/2)(k)((1)) and current superalgebra. osp(2/2)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2/2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2/2)(k)((1)) in the standard basis are obtained for arbitrary level k. (C) 2004 Elsevier B.V. All rights reserved.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Non-Perturbative Methods in Quantum Field Theory and Quantum Gravity

This thesis considers non-perturbative methods in quantum field theory with applications to gravity and cosmology. In particular, there are chapters on black hole holography, inflationary model building, and the conformal bootstrap.

Perturbative Ward identities for Yang-Mills field theory stochastically quantized

%'e compute the divergent part of the three-point vertex function of the non-Abelian Yang-Mills gauge field theory within the stochastic quantization approach to the one-loop order. This calculation allows us to find four renormalization constants which, together with the four previously obtained, verify, to the calculated order, some Ward identities.

Black hole scattering from Worldline Quantum Field Theory and the Classical Double Copy of Spinning particles

This PhD thesis focuses on studying the classical scattering of massive/massless particles toward black holes, and investigating double copy relations between classical observables in gauge theories and gravity. This is done in the Post-Minkowskian approximation i.e. a perturbative expansion of observables controlled by the gravitational coupling constant κ = 32πGN, with GN being the Newtonian coupling constant. The investigation is performed by using the Worldline Quantum Field Theory (WQFT), displaying a worldline path integral describing the scattering objects and a QFT path integral in the Born approximation, describing the intermediate bosons exchanged in the scattering event by the massive/massless particles. We introduce the WQFT, by deriving a relation between the Kosower- Maybee-O’Connell (KMOC) limit of amplitudes and worldline path integrals, then, we use that to study the classical Compton amplitude and higher point amplitudes. We also present a nice application of our formulation to the case of Hard Thermal Loops (HTL), by explicitly evaluating hard thermal currents in gauge theory and gravity. Next we move to the investigation of the classical double copy (CDC), which is a powerful tool to generate integrands for classical observables related to the binary inspiralling problem in General Relativity. In order to use a Bern-Carrasco-Johansson (BCJ) like prescription, straight at the classical level, one has to identify a double copy (DC) kernel, encoding the locality structure of the classical amplitude. Such kernel is evaluated by using a theory where scalar particles interacts through bi-adjoint scalars. We show here how to push forward the classical double copy so to account for spinning particles, in the framework of the WQFT. Here the quantization procedure on the worldline allows us to fully reconstruct the quantum theory on the gravitational side. Next we investigate how to describe the scattering of massless particles off black holes in the WQFT.

Quantum Riemannian geometry on graphs for gauge field theory

In questo lavoro estendiamo concetti classici della geometria Riemanniana al fine di risolvere le equazioni di Maxwell sul gruppo delle permutazioni $S_3$. Cominciamo dando la strutture algebriche di base e la definizione di calcolo differenziale quantico con le principali proprietà. Generalizziamo poi concetti della geometria Riemanniana, quali la metrica e l'algebra esterna, al caso quantico. Tutto ciò viene poi applicato ai grafi dando la forma esplicita del calcolo differenziale quantico su $\mathbb{K}(V)$, della metrica e Laplaciano del secondo ordine e infine dell'algebra esterna. A questo punto, riscriviamo le equazioni di Maxwell in forma geometrica compatta usando gli operatori e concetti della geometria differenziale su varietà che abbiamo generalizzato in precedenza. In questo modo, considerando l'elettromagnetismo come teoria di gauge, possiamo risolvere le equazioni di Maxwell su gruppi finiti oltre che su varietà differenziabili. In particolare, noi le risolviamo su $S_3$.

Philosophy of quantum field theory: an introduction with interviews and comments

In this thesis, I address quantum theories and specifically quantum field theories in their interpretive aspects, with the aim of capturing some of the most controversial and challenging issues, also in relation to possible future developments of physics. To do so, I rely on and review some of the discussions carried on in philosophy of physics, highlighting methodologies and goals. This makes the thesis an introduction to these discussions. Based on these arguments, I built and conducted 7 face-to-face interviews with physics professors and an online survey (which received 88 responses from master's and PhD students and postdoctoral researchers in physics), with the aim of understanding how physicists make sense of concepts related to quantum theories and to find out what they can add to the discussion. Of the data collected, I report a qualitative analysis through three constructed themes.

Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian dynamics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise

We study the dynamics of reaction-diffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Light-cone gauge integrals: prescriptionlessness at two loops

The only calculations performed beyond one-loop level in the light-cone gauge make use of the Mandelstam-Leibbrandt (ML) prescription in order to circumvent the notorious gauge dependent poles. Recently we have shown that in the context of negative dimensional integration method (NDIM) such prescription can be altogether abandoned, at least in one-loop order calculations. We extend our approach, now studying two-loop integrals pertaining to two-point functions. While previous works on the subject present only divergent parts for the integrals, we show that our prescriptionless method gives the same results for them, besides finite parts for arbitrary exponents of propagators. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Prescriptionless light-cone integrals

Perturbative quantum gauge field theory as seen within the perspective of physical gauge choices such as the light-cone gauge entails the emergence of troublesome poles of the type (k · n)-α in the Feynman integrals. These come from the boson field propagator, where α = 1, 2, ⋯ and nμ is the external arbitrary four-vector that defines the gauge proper. This becomes an additional hurdle in the computation of Feynman diagrams, since any graph containing internal boson lines will inevitably produce integrands with denominators bearing the characteristic gauge-fixing factor. How one deals with them has been the subject of research over decades, and several prescriptions have been suggested and tried in the course of time, with failures and successes. However, a more recent development at this fronteer which applies the negative dimensional technique to compute light-cone Feynman integrals shows that we can altogether dispense with prescriptions to perform the calculations. An additional bonus comes to us attached to this new technique, in that not only it renders the light-cone prescriptionless but, by the very nature of it, it can also dispense with decomposition formulas or partial fractioning tricks used in the standard approach to separate pole products of the type (k · n)-α[(k - p) · n]-β (β = 1, 2, ⋯). In this work we demonstrate how all this can be done.