A class of solvable models in Condensed Matter Physics

In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the Green's functions are obtained in terms of a finite number of parameters, to be self-consistently determined. Several examples are given. In particular, for these examples it is shown that in the one-dimensional case it is possible to derive by means of algebraic constraints a set of equations which allow us to determine the self-consistent parameters and to obtain a complete exact solution

Anomalous dimensions of spinning operators from conformal symmetry

We compute, to the first non-trivial order in the $\epsilon$-expansion of a perturbed scalar field theory, the anomalous dimensions of an infinite class of primary operators with arbitrary spin $\ell=0,1,..$, including as a particular case the weakly broken higher-spin currents, using only constraints from conformal symmetry. Following the bootstrap philosophy, no reference is made to any Lagrangian, equations of motion or coupling constants. Even the space dimensions d are left free. The interaction is implicitly turned on through the local operators by letting them acquire anomalous dimensions. When matching certain four-point and five-point functions with the corresponding quantities of the free field theory in the $\epsilon\to 0$ limit, no free parameter remains. It turns out that only the expected discrete d values are permitted and the ensuing anomalous dimensions reproduce known results for the weakly broken higher-spin currents and provide new results for the other spinning operators.Comment: 20 pages.v2: an important remark and references added, more examples include

The concept of ‘transcendence’ in modern Western philosophy and in twentieth century Hindu thought

‘Transcendence’ has been a key subject of Western philosophy of religion and history of ideas. The meaning of transcendence, however, has changed over time. The article looks at some perspectives o ered by the nineteenth and the twentieth century Anglo‐American and con‐ tinental European philosophers of religion and presents their views in relation to the concept of transcendence formulated by the Bengali Hindu traditionalist Bhaktisiddhanta Sarasvati (1874–1937). The questions raised are what transcendence in the philosophy of religion is, how one can speak of it, and what its goal is. The paper points to parallels and di erences in epistemology, ontology and practice. One di erence is that the nineteenth and the twentieth century Western philosophy of religion tended to assume an ontological di erence between self and transcendence inherited om personalities such as Søren Kierkegaard, but also to explore the concept of transcendence beyond the idea of a metaphysical God. Bhaktisiddhanta, whose foundational thought mirrors medieval Hindu philosophy of religion and the theistic schools of Vedānta, suggests that transcendence has a metaphysical and personal dimension that is to some degree ontologically similar to and directly knowable by the self. Bhaktisid‐ dhanta’s approach to transcendence di ers om Kierkegaard’s and other Western philosophers’ and revolves around the idea of God as a transcendent person that can be directly known mor‐ phologically and ontologically through devotion. The article is a contribution to the history of ideas and the philosophy of religion in Eurasia and beyond

Agents with dycotomic goals which generate a rank-size distribution

Many explanations have been proposed for the rank-size rule or power law in city size distribution based on a probabilistic process [4]. These explanations are usually opposed to that proposed by Zipf [11] who explained the rank-size rule as the result of the application of the principle of least effort. In his opinion, by using this principle, it is possible to find an equilibrium between the two opposite forces of diversification and of unification. In fact, because the main components of the system are resources, people and products, the first force brings people near to resources, and the latter brings products near to people. Even these notions are simple, and are accepted in the spatial economic field [5] it is not clear how a rank-size rule can be derived from it[2]. In this paper I will show how a rank-size distribution can be generated by using multiagent interaction which uses a probabilistic law to obtain opposing goals that correspond to unification and diversification forces. This paper is divided in two sections: the first section presents a model based on agents pursuing opposite goals; the second discusses the model in relation to the previously proposed models