DOI: 10.1007/bf01626516. Zeta function regularization of path integrals in curved spacetime

Zeta function regularization of path integrals in curved spacetime

10.1007/bf01626516

Crossref journal-article

Springer Science and Business Media LLC

Communications in Mathematical Physics (297)

Bibliography

Hawking, S. W. (1977). Zeta function regularization of path integrals in curved spacetime. Communications in Mathematical Physics, 55(2), 133â148.

Authors 1

S. W. Hawking (first)

References 25 Referenced 1,127

DeWitt, B.S.: Dynamical theory of groups and fields in relativity, groups and topology (eds. C. M. DeWitt and B. S. DeWitt). New York: Gordon and Breach 1964 / Dynamical theory of groups and fields in relativity, groups and topology by B.S. DeWitt (1964)
DeWitt, B.S.: Phys. Rep.19C, 295 (1975) (10.1016/0370-1573(75)90051-4) / Phys. Rep. by B.S. DeWitt (1975)
McKean, H.P., Singer, J.M.: J. Diff. Geo.5, 233–249 (1971) (10.4310/jdg/1214429791) / J. Diff. Geo. by H.P. McKean (1971)
Gilkey, P.B.: The index theorem and the heat equation. Boston: Publish or Perish 1974 / The index theorem and the heat equation by P.B. Gilkey (1974)
Candelas, P., Raine, D.J.: Phys. Rev. D12, 965–974 (1975) / Phys. Rev. by P. Candelas (1975)
Drummond, I.T.: Nucl. Phys.94B, 115–144 (1975) (10.1016/0550-3213(75)90089-9) / Nucl. Phys. by I.T. Drummond (1975)
Capper, D., Duff, M.: Nuovo Cimento23A, 173 (1974) (10.1007/BF02748300) / Nuovo Cimento by D. Capper (1974)
Duff, M., Deser, S., Isham, C.J.: Nucl. Phys.111B, 45 (1976) / Nucl. Phys. by M. Duff (1976)
Brown, L.S.: Stress tensor trace anomaly in a gravitational metric: scalar field. University of Washington, Preprint (1976)
Brown, L.S., Cassidy, J.P.: Stress tensor trace anomaly in a gravitational metric: General theory, Maxwell field. University of Washington, Preprint (1976) (10.1103/PhysRevD.15.2810)
Dowker, J.S., Critchley, R.: Phys. Rev. D13, 3224 (1976) / Phys. Rev. by J.S. Dowker (1976)
Dowker, J.S., Critchley, R.: The stress tensor conformal anomaly for scalar and spinor fields. University of Manchester, Preprint (1976) (10.1103/PhysRevD.16.3390)
Gibbons, G.W., Hawking, S.W.: Action integrals and partition functions in quantum gravity. Phys. Rev. D (to be published)
Manor, Y.: Complex Riemannian sections. University of Cambridge, Preprint (1977)
Feynman, R. P.: Magic without magic, (eds. J. A. Wheeler and J. Klaunder). San Francisco: W. H. Freeman 1972 / Magic without magic by R. P. Feynman (1972)
DeWitt, B.S.: Phys. Rev.162, 1195–1239 (1967) (10.1103/PhysRev.162.1195) / Phys. Rev. by B.S. DeWitt (1967)
Fadeev, L.D., Popov, V.N.: Usp. Fiz. Nauk111, 427–450 (1973) [English translation in Sov. Phys. Usp.16, 777–788 (1974)] (10.3367/UFNr.0111.197311b.0427) / Usp. Fiz. Nauk by L.D. Fadeev (1973)
Seeley, R.T.: Amer. Math. Soc. Proc. Symp. Pure Math.10, 288–307 (1967) (10.1090/pspum/010/0237943) / Amer. Math. Soc. Proc. Symp. Pure Math. by R.T. Seeley (1967)
Ray, D.B., Singer, I.M.: Advances in Math.7, 145–210 (1971) (10.1016/0001-8708(71)90045-4) / Advances in Math. by D.B. Ray (1971)
Gilkey, P.B.: Advanc. Math.15, 334–360 (1975) (10.1016/0001-8708(75)90141-3) / Advanc. Math. by P.B. Gilkey (1975)
'tHooft, G.: Phys. Rev. Letters37, 8–11 (1976) (10.1103/PhysRevLett.37.8) / Phys. Rev. Letters by G. 'tHooft (1976)
'tHooft, G.: Computation of the quantum effects due to a four dimensional pseudoparticle. Harvard University, Preprint
Hartle, J.B., Hawking, S.W.: Phys. Rev. D13, 2188–2203 (1976) / Phys. Rev. by J.B. Hartle (1976)
Adler, S., Lieverman, J., Ng, N.J.: Regularization of the stress-energy tensor for vector and scalar particles. Propagating in a general background metric. IAS Preprint (1976) (10.1016/0003-4916(77)90313-X)
Fulling, S.A., Christensen, S.: Trace anomalies and the Hawking effect. Kings College London, Preprint (1976)

Dates

Type	When
Created	20 years, 3 months ago (April 30, 2005, 9:55 p.m.)
Deposited	4 years, 1 month ago (July 10, 2021, 4:38 a.m.)
Indexed	2 weeks, 3 days ago (Aug. 7, 2025, 4:54 a.m.)
Issued	48 years, 2 months ago (June 1, 1977)
Published	48 years, 2 months ago (June 1, 1977)
Published Print	48 years, 2 months ago (June 1, 1977)

Funders 0

None

BibTeX

@article{Hawking_1977, title={Zeta function regularization of path integrals in curved spacetime}, volume={55}, ISSN={1432-0916}, url={http://dx.doi.org/10.1007/bf01626516}, DOI={10.1007/bf01626516}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Hawking, S. W.}, year={1977}, month=jun, pages={133–148} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        7
      ]
    ],
    "date-time": "2025-08-07T08:54:23Z",
    "timestamp": 1754556863436
  },
  "reference-count": 25,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "2",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1977,
            6,
            1
          ]
        ],
        "date-time": "1977-06-01T00:00:00Z",
        "timestamp": 233971200000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1977,
        6
      ]
    ]
  },
  "DOI": "10.1007/bf01626516",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        5,
        1
      ]
    ],
    "date-time": "2005-05-01T01:55:28Z",
    "timestamp": 1114912528000
  },
  "page": "133-148",
  "source": "Crossref",
  "is-referenced-by-count": 1127,
  "title": "Zeta function regularization of path integrals in curved spacetime",
  "prefix": "10.1007",
  "volume": "55",
  "author": [
    {
      "given": "S. W.",
      "family": "Hawking",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "CR1",
      "volume-title": "Dynamical theory of groups and fields in relativity, groups and topology",
      "author": "B.S. DeWitt",
      "year": "1964",
      "unstructured": "DeWitt, B.S.: Dynamical theory of groups and fields in relativity, groups and topology (eds. C. M. DeWitt and B. S. DeWitt). New York: Gordon and Breach 1964"
    },
    {
      "key": "CR2",
      "doi-asserted-by": "crossref",
      "first-page": "295",
      "DOI": "10.1016/0370-1573(75)90051-4",
      "volume": "19C",
      "author": "B.S. DeWitt",
      "year": "1975",
      "unstructured": "DeWitt, B.S.: Phys. Rep.19C, 295 (1975)",
      "journal-title": "Phys. Rep."
    },
    {
      "key": "CR3",
      "doi-asserted-by": "crossref",
      "first-page": "233",
      "DOI": "10.4310/jdg/1214429791",
      "volume": "5",
      "author": "H.P. McKean",
      "year": "1971",
      "unstructured": "McKean, H.P., Singer, J.M.: J. Diff. Geo.5, 233\u2013249 (1971)",
      "journal-title": "J. Diff. Geo."
    },
    {
      "key": "CR4",
      "volume-title": "The index theorem and the heat equation",
      "author": "P.B. Gilkey",
      "year": "1974",
      "unstructured": "Gilkey, P.B.: The index theorem and the heat equation. Boston: Publish or Perish 1974"
    },
    {
      "key": "CR5",
      "first-page": "965",
      "volume": "D12",
      "author": "P. Candelas",
      "year": "1975",
      "unstructured": "Candelas, P., Raine, D.J.: Phys. Rev. D12, 965\u2013974 (1975)",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "CR6",
      "doi-asserted-by": "crossref",
      "first-page": "115",
      "DOI": "10.1016/0550-3213(75)90089-9",
      "volume": "94B",
      "author": "I.T. Drummond",
      "year": "1975",
      "unstructured": "Drummond, I.T.: Nucl. Phys.94B, 115\u2013144 (1975)",
      "journal-title": "Nucl. Phys."
    },
    {
      "key": "CR7",
      "doi-asserted-by": "crossref",
      "first-page": "173",
      "DOI": "10.1007/BF02748300",
      "volume": "23A",
      "author": "D. Capper",
      "year": "1974",
      "unstructured": "Capper, D., Duff, M.: Nuovo Cimento23A, 173 (1974)",
      "journal-title": "Nuovo Cimento"
    },
    {
      "key": "CR8",
      "first-page": "45",
      "volume": "111B",
      "author": "M. Duff",
      "year": "1976",
      "unstructured": "Duff, M., Deser, S., Isham, C.J.: Nucl. Phys.111B, 45 (1976)",
      "journal-title": "Nucl. Phys."
    },
    {
      "key": "CR9",
      "unstructured": "Brown, L.S.: Stress tensor trace anomaly in a gravitational metric: scalar field. University of Washington, Preprint (1976)"
    },
    {
      "key": "CR10",
      "doi-asserted-by": "crossref",
      "unstructured": "Brown, L.S., Cassidy, J.P.: Stress tensor trace anomaly in a gravitational metric: General theory, Maxwell field. University of Washington, Preprint (1976)",
      "DOI": "10.1103/PhysRevD.15.2810"
    },
    {
      "key": "CR11",
      "first-page": "3224",
      "volume": "D13",
      "author": "J.S. Dowker",
      "year": "1976",
      "unstructured": "Dowker, J.S., Critchley, R.: Phys. Rev. D13, 3224 (1976)",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "CR12",
      "doi-asserted-by": "crossref",
      "unstructured": "Dowker, J.S., Critchley, R.: The stress tensor conformal anomaly for scalar and spinor fields. University of Manchester, Preprint (1976)",
      "DOI": "10.1103/PhysRevD.16.3390"
    },
    {
      "key": "CR13",
      "unstructured": "Gibbons, G.W., Hawking, S.W.: Action integrals and partition functions in quantum gravity. Phys. Rev. D (to be published)"
    },
    {
      "key": "CR14",
      "unstructured": "Manor, Y.: Complex Riemannian sections. University of Cambridge, Preprint (1977)"
    },
    {
      "key": "CR15",
      "volume-title": "Magic without magic",
      "author": "R. P. Feynman",
      "year": "1972",
      "unstructured": "Feynman, R. P.: Magic without magic, (eds. J. A. Wheeler and J. Klaunder). San Francisco: W. H. Freeman 1972"
    },
    {
      "key": "CR16",
      "doi-asserted-by": "crossref",
      "first-page": "1195",
      "DOI": "10.1103/PhysRev.162.1195",
      "volume": "162",
      "author": "B.S. DeWitt",
      "year": "1967",
      "unstructured": "DeWitt, B.S.: Phys. Rev.162, 1195\u20131239 (1967)",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "CR17",
      "doi-asserted-by": "crossref",
      "first-page": "427",
      "DOI": "10.3367/UFNr.0111.197311b.0427",
      "volume": "111",
      "author": "L.D. Fadeev",
      "year": "1973",
      "unstructured": "Fadeev, L.D., Popov, V.N.: Usp. Fiz. Nauk111, 427\u2013450 (1973) [English translation in Sov. Phys. Usp.16, 777\u2013788 (1974)]",
      "journal-title": "Usp. Fiz. Nauk"
    },
    {
      "key": "CR18",
      "doi-asserted-by": "crossref",
      "first-page": "288",
      "DOI": "10.1090/pspum/010/0237943",
      "volume": "10",
      "author": "R.T. Seeley",
      "year": "1967",
      "unstructured": "Seeley, R.T.: Amer. Math. Soc. Proc. Symp. Pure Math.10, 288\u2013307 (1967)",
      "journal-title": "Amer. Math. Soc. Proc. Symp. Pure Math."
    },
    {
      "key": "CR19",
      "doi-asserted-by": "crossref",
      "first-page": "145",
      "DOI": "10.1016/0001-8708(71)90045-4",
      "volume": "7",
      "author": "D.B. Ray",
      "year": "1971",
      "unstructured": "Ray, D.B., Singer, I.M.: Advances in Math.7, 145\u2013210 (1971)",
      "journal-title": "Advances in Math."
    },
    {
      "key": "CR20",
      "doi-asserted-by": "crossref",
      "first-page": "334",
      "DOI": "10.1016/0001-8708(75)90141-3",
      "volume": "15",
      "author": "P.B. Gilkey",
      "year": "1975",
      "unstructured": "Gilkey, P.B.: Advanc. Math.15, 334\u2013360 (1975)",
      "journal-title": "Advanc. Math."
    },
    {
      "key": "CR21",
      "doi-asserted-by": "crossref",
      "first-page": "8",
      "DOI": "10.1103/PhysRevLett.37.8",
      "volume": "37",
      "author": "G. 'tHooft",
      "year": "1976",
      "unstructured": "'tHooft, G.: Phys. Rev. Letters37, 8\u201311 (1976)",
      "journal-title": "Phys. Rev. Letters"
    },
    {
      "key": "CR22",
      "unstructured": "'tHooft, G.: Computation of the quantum effects due to a four dimensional pseudoparticle. Harvard University, Preprint"
    },
    {
      "key": "CR23",
      "first-page": "2188",
      "volume": "D13",
      "author": "J.B. Hartle",
      "year": "1976",
      "unstructured": "Hartle, J.B., Hawking, S.W.: Phys. Rev. D13, 2188\u20132203 (1976)",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "CR24",
      "doi-asserted-by": "crossref",
      "unstructured": "Adler, S., Lieverman, J., Ng, N.J.: Regularization of the stress-energy tensor for vector and scalar particles. Propagating in a general background metric. IAS Preprint (1976)",
      "DOI": "10.1016/0003-4916(77)90313-X"
    },
    {
      "key": "CR25",
      "unstructured": "Fulling, S.A., Christensen, S.: Trace anomalies and the Hawking effect. Kings College London, Preprint (1976)"
    }
  ],
  "container-title": "Communications in Mathematical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01626516.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/article/10.1007/BF01626516/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01626516",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2021,
        7,
        10
      ]
    ],
    "date-time": "2021-07-10T08:38:12Z",
    "timestamp": 1625906292000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "http://link.springer.com/10.1007/BF01626516"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1977,
        6
      ]
    ]
  },
  "references-count": 25,
  "journal-issue": {
    "issue": "2",
    "published-print": {
      "date-parts": [
        [
          1977,
          6
        ]
      ]
    }
  },
  "alternative-id": [
    "BF01626516"
  ],
  "URL": "http://dx.doi.org/10.1007/BF01626516",
  "relation": {},
  "ISSN": [
    "0010-3616",
    "1432-0916"
  ],
  "subject": [],
  "container-title-short": "Commun.Math. Phys.",
  "published": {
    "date-parts": [
      [
        1977,
        6
      ]
    ]
  }
}