Skip to main content
Log in

Implications of Poincaré symmetry for thermal field theories in finite-volume

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

The analytic continuation to an imaginary velocity i ξ of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. Writing the Boltzmann factor as , the Poincaré invariance underlying a relativistic theory implies a dependence of the free-energy on L 0 and the shift ξ only through the combination . This in turn implies a set of Ward identities, some of which were previously derived by us, among the correlators of the energy-momentum tensor. In the infinite-volume limit they lead to relations among the cumulants of the total energy distribution and those of the momentum, i.e. they connect the energy and the momentum distributions in the canonical ensemble. In finite volume the Poincaré symmetry translates into exact relations among partition functions and correlation functions defined with different sets of (generalized) periodic boundary conditions. They have interesting applications in lattice field theory. In particular, they offer Ward identities to renormalize non-perturbatively the energy-momentum tensor and novel ways to compute thermodynamic potentials. At fixed bare parameters they also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Giusti and H.B. Meyer, Thermal momentum distribution from path integrals with shifted boundary conditions, Phys. Rev. Lett. 106 (2011) 131601 [arXiv:1011.2727] [INSPIRE].

    Article  ADS  Google Scholar 

  2. L. Giusti and H.B. Meyer, Thermodynamic potentials from shifted boundary conditions: the scalar-field theory case, JHEP 11 (2011) 087 [arXiv:1110.3136] [INSPIRE].

    Article  ADS  Google Scholar 

  3. L. Landau and E. Lifshitz, Course of theoretical physics VI: fluid mechanics, Butterworth-Heinemann, Oxford U.K. (1987).

    MATH  Google Scholar 

  4. L. Landau and E. Lifshitz, Course of theoretical physics X: physical kinetics, Butterworth-Heinemann, Oxford U.K. (1981).

    Google Scholar 

  5. H. Ott, Lorentz-Transformation der Wärme und der Temperatur (in German), Z. Phys. 175 (1963) 70.

  6. H. Arzeliès, Transformation relativiste de la temperature et de quelques autres grandeurs thermodynamiques, Nuovo Cim. 35 (1965) 792.

    Article  Google Scholar 

  7. M. Przanowski and J. Tosiek, Notes on thermodynamics in special relativity, Phys. Scripta 84 (2011) 055008 [arXiv:1010.5701].

    Article  ADS  Google Scholar 

  8. M. Della Morte and L. Giusti, A novel approach for computing glueball masses and matrix elements in Yang-Mills theories on the lattice, JHEP 05 (2011) 056 [arXiv:1012.2562] [INSPIRE].

    Article  ADS  Google Scholar 

  9. H.B. Meyer, Finite volume effects in thermal field theory, JHEP 07 (2009) 059 [arXiv:0905.1663] [INSPIRE].

    Article  ADS  Google Scholar 

  10. S. Caracciolo, G. Curci, P. Menotti and A. Pelissetto, The energy momentum tensor for lattice gauge theories, Annals Phys. 197 (1990) 119 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  11. S. Caracciolo, G. Curci, P. Menotti and A. Pelissetto, The energy momentum tensor on the lattice: the scalar case, Nucl. Phys. B 309 (1988) 612 [INSPIRE].

    Article  ADS  Google Scholar 

  12. M. Lüscher, S. Sint, R. Sommer and P. Weisz, Chiral symmetry and O(a) improvement in lattice QCD, Nucl. Phys. B 478 (1996) 365 [hep-lat/9605038] [INSPIRE].

    Article  ADS  Google Scholar 

  13. O. Philipsen, The QCD equation of state from the lattice, arXiv:1207.5999 [INSPIRE].

  14. J. Engels, J. Fingberg, F. Karsch, D. Miller and M. Weber, Nonperturbative thermodynamics of SU(N) gauge theories, Phys. Lett. B 252 (1990) 625 [INSPIRE].

    ADS  Google Scholar 

  15. S. Borsányi, G. Endrodi, Z. Fodor, S. Katz and K. Szabo, Precision SU(3) lattice thermodynamics for a large temperature range, JHEP 07 (2012) 056 [arXiv:1204.6184] [INSPIRE].

    Article  ADS  Google Scholar 

  16. T. Umeda et al., Fixed scale approach to equation of state in lattice QCD, Phys. Rev. D 79 (2009) 051501 [arXiv:0809.2842] [INSPIRE].

    ADS  Google Scholar 

  17. B.B. Brandt, A. Francis, H.B. Meyer, H. Wittig and O. Philipsen, QCD thermodynamics with two flavours of Wilson fermions on large lattices, arXiv:1210.6972 [INSPIRE].

  18. H. Elze, K. Kajantie and J.I. Kapusta, Screening and plasmon in QCD on a finite lattice, Nucl. Phys. B 304 (1988) 832 [INSPIRE].

    Article  ADS  Google Scholar 

  19. H.B. Meyer, Energy-momentum tensor correlators and viscosity, PoS(LATTICE 2008)017 [arXiv:0809.5202] [INSPIRE].

  20. H.B. Meyer, Cutoff effects on energy-momentum tensor correlators in lattice gauge theory, JHEP 06 (2009) 077 [arXiv:0904.1806] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Harvey B. Meyer.

Additional information

ArXiv ePrint: 1211.6669

Rights and permissions

Reprints and permissions

About this article

Cite this article

Giusti, L., Meyer, H.B. Implications of Poincaré symmetry for thermal field theories in finite-volume. J. High Energ. Phys. 2013, 140 (2013). https://doi.org/10.1007/JHEP01(2013)140

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP01(2013)140

Keywords

Navigation