% =============================================================================
% BibTeX Bibliography for:
% "Existence of a Mass Gap in Lattice Yang-Mills Theory:
%  A Discrete Formulation of the Millennium Problem"
% Author: Rafael D. De Paz
% =============================================================================

% --- Yang-Mills Foundation ---

@article{YangMills1954,
  author    = {Yang, Chen-Ning and Mills, Robert L.},
  title     = {Conservation of Isotopic Spin and Isotopic Gauge Invariance},
  journal   = {Physical Review},
  volume    = {96},
  number    = {1},
  pages     = {191--195},
  year      = {1954},
  doi       = {10.1103/PhysRev.96.191}
}

@misc{ClayYM,
  author    = {{Clay Mathematics Institute}},
  title     = {Yang-{M}ills and Mass Gap},
  year      = {2000},
  url       = {https://www.claymath.org/millennium/yang-mills-the-maths-gap/},
  note      = {Millennium Prize Problem, official problem statement by A.~Jaffe and E.~Witten}
}

@article{JaffeWitten2000,
  author    = {Jaffe, Arthur and Witten, Edward},
  title     = {Quantum {Y}ang-{M}ills Theory},
  journal   = {Clay Mathematics Institute Millennium Prize Problems},
  year      = {2000},
  pages     = {129--152},
  url       = {https://www.claymath.org/millennium/yang-mills-the-maths-gap/}
}

% --- Lattice Gauge Theory ---

@article{Wilson1974,
  author    = {Wilson, Kenneth G.},
  title     = {Confinement of quarks},
  journal   = {Physical Review D},
  volume    = {10},
  number    = {8},
  pages     = {2445--2459},
  year      = {1974},
  doi       = {10.1103/PhysRevD.10.2445}
}

@book{CreutzBook,
  author    = {Creutz, Michael},
  title     = {Quarks, Gluons and Lattices},
  publisher = {Cambridge University Press},
  year      = {1983},
  isbn      = {978-0-521-31535-7}
}

@book{MontvayMunster,
  author    = {Montvay, Istv\'an and M\"unster, Gernot},
  title     = {Quantum Fields on a Lattice},
  publisher = {Cambridge University Press},
  year      = {1994},
  isbn      = {978-0-521-59917-7}
}

@book{RotheBook,
  author    = {Rothe, Heinz J.},
  title     = {Lattice Gauge Theories: An Introduction},
  publisher = {World Scientific},
  year      = {2012},
  edition   = {4th},
  isbn      = {978-981-4365-87-1}
}

@article{OsterwalderSeiler1978,
  author    = {Osterwalder, Konrad and Seiler, Erhard},
  title     = {Gauge field theories on a lattice},
  journal   = {Annals of Physics},
  volume    = {110},
  number    = {2},
  pages     = {440--471},
  year      = {1978},
  doi       = {10.1016/0003-4916(78)90039-8}
}

% --- Mass Gap and Confinement ---

@article{BalianDrouffeItzykson1975,
  author    = {Balian, R. and Drouffe, J. M. and Itzykson, C.},
  title     = {Gauge fields on a lattice. II. Gauge-invariant {I}sing model},
  journal   = {Physical Review D},
  volume    = {11},
  number    = {8},
  pages     = {2098--2103},
  year      = {1975},
  doi       = {10.1103/PhysRevD.11.2098}
}

@article{GlimmJaffe1981,
  author    = {Glimm, James and Jaffe, Arthur},
  title     = {Quantum Physics: A Functional Integral Point of View},
  publisher = {Springer-Verlag},
  year      = {1981},
  journal   = {New York}
}

@article{Fredenhagen1985,
  author    = {Fredenhagen, Klaus and Marcu, Mihail},
  title     = {Confinement criterion for {QCD} with dynamical quarks},
  journal   = {Physical Review Letters},
  volume    = {56},
  number    = {3},
  pages     = {223--224},
  year      = {1986},
  doi       = {10.1103/PhysRevLett.56.223}
}

% --- Transfer Matrix and Spectral Gap ---

@article{LuscherWeisz2002,
  author    = {L\"uscher, Martin and Weisz, Peter},
  title     = {Locality and exponential error reduction in numerical lattice gauge theory},
  journal   = {Journal of High Energy Physics},
  volume    = {2001},
  number    = {09},
  pages     = {010},
  year      = {2001},
  doi       = {10.1088/1126-6708/2001/09/010}
}

@article{Luscher1977,
  author    = {L\"uscher, Martin},
  title     = {Construction of a selfadjoint, strictly positive transfer matrix for {E}uclidean lattice gauge theories},
  journal   = {Communications in Mathematical Physics},
  volume    = {54},
  pages     = {283--292},
  year      = {1977},
  doi       = {10.1007/BF01614090}
}

% --- Osterwalder-Schrader and Wightman Axioms ---

@article{OsterwalderSchrader1973,
  author    = {Osterwalder, Konrad and Schrader, Robert},
  title     = {Axioms for {E}uclidean {G}reen's functions},
  journal   = {Communications in Mathematical Physics},
  volume    = {31},
  pages     = {83--112},
  year      = {1973},
  doi       = {10.1007/BF01645738}
}

@article{OsterwalderSchrader1975,
  author    = {Osterwalder, Konrad and Schrader, Robert},
  title     = {Axioms for {E}uclidean {G}reen's functions. {II}},
  journal   = {Communications in Mathematical Physics},
  volume    = {42},
  pages     = {281--305},
  year      = {1975},
  doi       = {10.1007/BF01608978}
}

@book{Wightman1964,
  author    = {Streater, R. F. and Wightman, A. S.},
  title     = {{PCT}, Spin and Statistics, and All That},
  publisher = {W. A. Benjamin},
  year      = {1964}
}

% --- Renormalization and Asymptotic Freedom ---

@article{GrossWilczek1973,
  author    = {Gross, David J. and Wilczek, Frank},
  title     = {Ultraviolet Behavior of Non-{A}belian Gauge Theories},
  journal   = {Physical Review Letters},
  volume    = {30},
  number    = {26},
  pages     = {1343--1346},
  year      = {1973},
  doi       = {10.1103/PhysRevLett.30.1343}
}

@article{Politzer1973,
  author    = {Politzer, H. David},
  title     = {Reliable Perturbative Results for Strong Interactions?},
  journal   = {Physical Review Letters},
  volume    = {30},
  number    = {26},
  pages     = {1346--1349},
  year      = {1973},
  doi       = {10.1103/PhysRevLett.30.1346}
}

% --- Quantum Gravity / Planck Scale ---

@article{Planck1899,
  author    = {Planck, Max},
  title     = {\"Uber irreversible {S}trahlungsvorga\"nge},
  journal   = {Sitzungsberichte der K\"oniglich Preu\ss{}ischen Akademie
               der Wissenschaften zu Berlin},
  year      = {1899},
  pages     = {440--480}
}

@article{Rovelli2004,
  author    = {Rovelli, Carlo},
  title     = {Quantum Gravity},
  publisher = {Cambridge University Press},
  year      = {2004},
  journal   = {Cambridge Monographs on Mathematical Physics}
}

% --- Functional Analysis ---

@book{ReedSimon1975,
  author    = {Reed, Michael and Simon, Barry},
  title     = {Methods of Modern Mathematical Physics. {II}: {F}ourier Analysis, Self-Adjointness},
  publisher = {Academic Press},
  year      = {1975}
}

@book{Simon2005,
  author    = {Simon, Barry},
  title     = {Functional Integration and Quantum Physics},
  publisher = {AMS Chelsea Publishing},
  year      = {2005},
  edition   = {2nd}
}


@article{th2000quantum,
  title={Quantum Yang-Mills theory},
  author={Jaffe, Arthur and Witten, Edward},
  journal={Clay Mathematics Institute},
  year={2000}
}
@article{gross1973ultraviolet,
  title={Ultraviolet behavior of non-abelian gauge theories},
  author={Gross, David J and Wilczek, Frank},
  journal={Physical Review Letters},
  volume={30},
  number={26},
  pages={1343},
  year={1973},
  publisher={APS}
}