Phi-Psi model for Electrodynamics in dielectric media: exact quantisation in the Heisenberg representation

We investigate the quantization in the Heisenberg representation of a model which represents a simplification of the Hopfield model for dielectric media, where the electromagnetic field is replaced by a scalar field $\phi$ and the role of the polarization field is played by a further scalar field $\psi$. The model, which is quadratic in the fields, is still characterized by a nontrivial physical content, as the physical particles correspond to the polaritons of the standard Hopfield model of condensed matter physics. Causality is also taken into account and a discussion of the standard interaction representation is also considered.Comment: 9 page

Exact quantisation of the relativistic Hopfield model

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields. The matter fields are represented by a mesoscopic polarization field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalized Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.Comment: 24 page

Path integral quantization of the relativistic Hopfield model

The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path integral formalism. In particular we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.Comment: 16 page

Super-Ego after Freud: A Lesson not to Be Forgotten

The aim of this paper is to retrace the evolution of the super-ego, in psychoanalysis and phenomenology, describing its effects on education, starting with the formation of individual morality. In the broadest sense, the reflection concerns not only the role that the family can play in this direction, but above all the contribution that schools can make to the formation of individual morality. The structuring of the super-ego is thus built up in the family system by being influenced by the socio-educational environment. The importance of a healthy structuring of the super-ego emerges in the increased risk of alteration of the intersubjective sphere, in cases of dysregulation of the super-ego, a process that is fundamental to psychotic disorder

Functioning of Declarative Memory: Intersection between Neuropsychology and Mathematics

The understanding of memory has been a constant challenge for scientific research for centuries. The mnemonic processes, which determine the identity of the human being, have been investigated through multiple points of view, such as the psychological, neurophysiological and physical ones. The result is complex and multifaceted visions that should be integrated to provide a unitary and complete interpretation. A survey of the most recent scientific literature is carried out on the functioning of declarative memory, to analyse the relationship between real information coming from the outside world, the encoded event and the recovered memory. The aim of the essay is to investigate the neural correlates, which regulate the cognitive system in question, through a dual neuropsychological-mathematical interpretation. Neuropsychology sheds light on the anatomical, physiological and psychic mechanisms of memory while Mathematics associates the corresponding mathematical configurations to neural networks. The reunification process between the two disciplines is achieved  through neuromorphic computational simulation that emulates mind uploading. The assembly of artificial neurons has the potential to clarify in detail the memory processes, the functioning of neural correlates and to carry out the mapping of the biological brain. We hope that the results obtained will provide new knowledge on mnestic mechanisms to contribute to the evolution of disciplines such as General Psychology, Forensic Neuroscience, Cognitive Rehabilitation and Awake Surgery

Monaci e signori nella valle sublacense in epoca medievale: architettura monastica e signorile. Analisi e documentazione archeologica delle strutture edilizie per una geografia del costruito

La ricerca proposta comprende quale area di interesse l’archeologia dell’architettura e intende rispondere a determinate domande ancora aperte sulle metodologie costruttive, sulle committenze, sulle maestranze e sulle influenze stilistiche esterne che nel corso del medioevo, dal X al XVI secolo, hanno segnato l’Abbazia di Subiaco e i suoi possedimenti, analizzando l’architettura laica e quella monastica