Research

A brief description of my research intersts:

  • Algebraic approach to quantum field theory in curved space-times (holography, perturbative aspects, influence of boundary conditions);
  • Relativistic classical field theory (rigorous functional aspects, geometric analysis of hyperbolic Euler-Lagrange equations, deformation quantization);
  • Global Lorentzian geometry (null rigidity, causal structure, analytical properties of Lorentzian distance function).

Publication list:

  • R. Brunetti, K. Fredenhagen, P. L. Ribeiro, Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields. Commun. Math. Phys. 368 (2019) 519-584. DOI:10.1007/s00220-019-03454-z, arXiv:1209.2148 [math-ph].
  • P. L. Ribeiro. Algebraic holography in asymptotically simple, asymptotically AdS spacetimes. Contribution to the Proceedings of the Symposium “Rigorous Quantum Field Theory”, in the honour of the 70th birthday of Prof. Jacques Bros (SPhT – CEA-Saclay, Paris, France, 19-21 July 2004). Progress in Mathematics 251 (Birkhäuser, 2007), pp. 253-270. DOI:10.1007/978-3-7643-7434-1_18, arXiv:hep-th/0502096.
  • P. L. Ribeiro. Conserved gravitational charges, locality and the holographic Weyl anomaly – a fresh viewpoint. Contribuição para os Proceedings of the International Conference “100 Years of Relativity” (MASP, São Paulo, Brazil, 22-24 August 2005). Braz. J. Phys. 35 (2005) 1133-1135. DOI:10.1590/S0103-97332005000700033, arXiv:gr-qc/0510082.
  • P. L. Ribeiro. Renormalization Group Flow in Algebraic Holography. In: Proceedings of the International Conference on Renormalization Group and Anomalies in Gravity and Cosmology (M. Asorey, I.L. Shapiro, eds.). Nucl. Phys. B Proc. Suppl. 127 (2004) 193-195. DOI:10.1016/S0920-5632(03)02430-7, arXiv:hep-th/0306024.

PhD Thesis (2007):

  • P. L. Ribeiro. Structural and Dynamical Aspects of the AdS/CFT Correspondence: a Rigorous Approach. Corrected English translation (with errata), University of São Paulo, 2007. arXiv:0712.0401 [math-ph].

Preprints:

Portuguese version