References

HK1986

T. M. Helliwell and D. A. Konkowski, Vacuum fluctuations outside cosmic strings, Physical Review D 34 (1986), 1918–1920. DOI: 10.1103/PhysRevD.34.1918. {$‡$}

Linet1987

B. Linet, Quantum field theory in the space-time of a cosmic string, Physical Review D 35 (1987), 536. DOI: 10.1103/PhysRevD.35.536. The supplied records disagree on the last page; only the first page is used here. {$‡$}

FS1987

V. P. Frolov and E. M. Serebriany, Vacuum polarization in the gravitational field of a cosmic string, Physical Review D 35 (1987), 3779–3782. DOI: 10.1103/PhysRevD.35.3779. {$‡$}

Dowker1987

J. S. Dowker, Casimir effect around a cone, Physical Review D 36 (1987), 3095–3101. DOI: 10.1103/PhysRevD.36.3095. {$‡$}

Dowker1987b

J. S. Dowker, Vacuum averages for arbitrary spin around a cosmic string, Physical Review D 36 (1987), 3742–3746. {$‡$}

GL1994

M. E. X. Guimarães and B. Linet, Scalar Green's functions in an Euclidean space with a conical-type line singularity, Communications in Mathematical Physics 165 (1994), 297–310. DOI: 10.1007/BF02099773. {$‡$}

Guimaraes1995

M. E. X. Guimarães, Vacuum polarization at finite temperature around a magnetic flux cosmic string, Classical and Quantum Gravity 12 (1995), 1705–1714. DOI: 10.1088/0264-9381/12/7/012. https://arxiv.org/abs/gr-qc/9502003. Used: the zero-temperature formulas (19), (30), and the displayed ${\omega }_2,{\omega }_4$ coefficients.

Sriramkumar2001

L. Sriramkumar, Fluctuations in the current and energy densities around a magnetic-flux-carrying cosmic string, Classical and Quantum Gravity 18 (2001), 1015. DOI: 10.1088/0264-9381/18/6/304. https://arxiv.org/abs/gr-qc/0011074. {$\ast$} Used: (2.4), (2.10)–(2.16).

SBdM2003

J. Spinelly and E. R. Bezerra de Mello, Vacuum polarization of a charged massless scalar field on cosmic string spacetime in the presence of a magnetic field, Classical and Quantum Gravity 20 (2003), 873–887. https://arxiv.org/abs/hep-th/0301169. {$\ast$} Used: (22), (30), (36), (37), (54)–(56), (68). Equations (30) and (36) agree with $F$. The printed equation (37) has denominator $48{\pi }^2{\alpha }^4{r}^2$, an extra ${\alpha }^{-2}$, and does not agree. The earlier agreement claim for (37) was our transcription error. The printed discrepancy in (55) is discussed explicitly and is retained.

BdMBSH2015

E. R. Bezerra de Mello, V. B. Bezerra, A. A. Saharian, and H. H. Harutyunyan, Vacuum currents induced by a magnetic flux around a cosmic string with finite core, Physical Review D 91 (2015), 064034. https://arxiv.org/abs/1411.1258. {$\ast$} Used: (2.8)–(2.10), (3.4), and (4.2)–(4.7).

KayStuder

B. S. Kay and U. M. Studer, Boundary conditions for quantum mechanics on cones and fields around cosmic strings, Communications in Mathematical Physics 139 (1991), 103–139. DOI: 10.1007/BF02102731. {$‡$}

DR2017

J. Dereziński and S. Richard, On Schrödinger operators with inverse square potentials on the half-line, Annales Henri Poincaré 18 (2017), 869–928. DOI: 10.1007/s00023-016-0520-7. https://arxiv.org/abs/1604.03340.

AKO1996

B. Allen, B. S. Kay, and A. C. Ottewill, Long-range effects of cosmic string structure, Physical Review D 53 (1996), 6829–6841. DOI: 10.1103/PhysRevD.53.6829. https://arxiv.org/abs/gr-qc/9510058. {$\ast$} Used: (3.7), (3.17), (4.3), (4.8), (4.13)–(4.17), and Appendix A.

FM2007

C. Filgueiras and F. Moraes, The bound-state Aharonov–Bohm effect around a cosmic string revisited, Physics Letters A 361 (2007), 13–15. DOI: 10.1016/j.physleta.2006.09.030. https://arxiv.org/abs/gr-qc/0509100. {$\ast$} Used: (8), (10).

AllenOttewill1990

B. Allen and A. C. Ottewill, Effects of curvature couplings for quantum fields on cosmic-string space-times, Physical Review D 42 (1990), 2669–2677. {$‡$}

SouradeepSahni

T. Souradeep and V. Sahni, Quantum effects near a point mass in $2+1$-dimensional gravity, Physical Review D 46 (1992), 1616–1633. {$†$}

Smith1990

A. G. Smith, Gravitational effects of an infinite straight cosmic string on classical and quantum fields: self-force and vacuum fluctuations, in G. W. Gibbons, S. W. Hawking, and T. Vachaspati, eds., The Formation and Evolution of Cosmic Strings, Cambridge University Press, 1990, pp. 263–292. {$‡$} The supplied AB/SAE records note a 1989 citation in SBdM2003; this variation is not resolved here.

SousaGerbert1989

Ph. de Sousa Gerbert, Fermions in an Aharonov–Bohm field and cosmic strings, Physical Review D 40 (1989), 1346–1349. {$‡$}

BordagVoropaev1993

M. Bordag and S. Voropaev, Charged particle with magnetic moment in the Aharonov–Bohm potential, Journal of Physics A 26 (1993), 7637–7649. https://arxiv.org/abs/hep-th/9304017. {$‡$}

BdFS1999

C. G. Beneventano, M. De Francia, and E. M. Santangelo, Dirac fields in the background of a magnetic flux string and spectral boundary conditions, International Journal of Modern Physics A 14 (1999), 4749–4762. https://arxiv.org/abs/hep-th/9809081. {$‡$}

CheegerTaylor

J. Cheeger and M. Taylor, On the diffraction of waves by conical singularities. I, II, Communications on Pure and Applied Mathematics 35 (1982), 275–331 and 487–529.

Watson

G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd edition, Cambridge University Press, 1944.

GR

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th edition, Academic Press, 2007. {$†$}

DLMF

F. W. J. Olver et al., eds., NIST Digital Library of Mathematical Functions. Used: Bessel representations, transforms, and Struve integrals, especially Sections 10.22, 10.32, 10.43, and 11.5. https://dlmf.nist.gov/.

MorreyNirenberg

C. B. Morrey, Jr., and L. Nirenberg, On the analyticity of the solutions of linear elliptic systems of partial differential equations, Communications on Pure and Applied Mathematics 10 (1957), 271–290. DOI: 10.1002/cpa.3160100204.

Hormander

L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, 2nd edition, Springer, 1990.

ReedSimonII

M. Reed and B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press, 1975. {$†$}

Wald1977

R. M. Wald, The back reaction effect in particle creation in curved spacetime, Communications in Mathematical Physics 54 (1977), 1–19.

Wald1978

R. M. Wald, Trace anomaly of a conformally invariant quantum field in curved spacetime, Physical Review D 17 (1978), 1477–1484. {$†$}

Wald1994

R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, University of Chicago Press, 1994.

HollandsWald2001

S. Hollands and R. M. Wald, Local Wick polynomials and time ordered products of quantum fields in curved spacetime, Communications in Mathematical Physics 223 (2001), 289–326. DOI: 10.1007/s002200100540. https://arxiv.org/abs/gr-qc/0103074.

HollandsWald2005

S. Hollands and R. M. Wald, Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes, Reviews in Mathematical Physics 17 (2005), 227–312. https://arxiv.org/abs/gr-qc/0404074.

DecaniniFolacci

Y. Décanini and A. Folacci, Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension, Physical Review D 78 (2008), 044025. DOI: 10.1103/PhysRevD.78.044025. https://arxiv.org/abs/gr-qc/0512118.

Radzikowski

M. J. Radzikowski, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Communications in Mathematical Physics 179 (1996), 529–553.

KayWald

B. S. Kay and R. M. Wald, Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate Killing horizon, Physics Reports 207 (1991), 49–136. {$†$}

Retained manuscript records and scoped companion references. These entries identify the supplied records or documentary interfaces. They do not assert independent verification of entire companion manuscripts or transfer of their mathematical constructions.

RecordVP2

N. Cheung, I-B-VP: Vacuum polarization of the Friedrichs ground state on a prescribed conical spacetime, supplied -B-VP-v2.tex, October 2026. Retained source for the heat estimate, all-diagonal analytic subtraction, local renormalization, transfer separation, finite reporting, and integrity discipline.

RecordAB

N. Cheung, I-B-VP-AB: Vacuum polarization and induced current of the Friedrichs ground state on the conical Enter spacetime, supplied -B-VP-AB.tex, October 2026. Retained AB successor record, called version 2 in that source.

RecordSAE

N. Cheung, I-B-VP-SAE: Closing the self-adjoint extension ledger, supplied -B-VP-SAE.tex, October 2026. Retained extension-ledger record, called version 3 in that source. Its qualifications and corrections are stated in the present text.

CheungEnter

N. Cheung, The Enter Calculus: A Linear Quantum Lambda Calculus with an Operational Characterization of Measurement, supplied bibliographic record: Frontiers in Physics 14 (2026), article 1954943. DOI: 10.3389/fphy.2026.1954943. The supplied source describes a publisher accepted-article record. Current publication status is not independently asserted here. Cited only for finite operational semantics.

CheungPhil

N. Cheung, The Philosophy of Enter: Destructive Readout, Quantum Recovery, and the Refusal of Identification, supplied source identifier -v2.tex. Documentary orientation, not a continuum theorem premise.

CheungIB

N. Cheung, I-B-v1: A Finite Enter Spacetime: Calibrated Destructive Time Readout on a Prescribed Conical Product, version 1, Enter Calculus Companion. Used: prescribed host, :not-source, and :instrument. https://enter.grok.me/browse/I-B.

CheungIBG

N. Cheung, I-B-G: Intrinsic and holonomy-twisted Green operators on a prescribed conical spacetime: Self-adjoint extensions, diffraction, finite propagation, and supported transfer from flat-completion laboratories, supplied -B-G-v2.tex, October 2026. The earlier AB/SAE records use a different title and theorem numbering for -B-G.tex. Relevant source labels are identified in Section sec:background.

CheungXAST

N. Cheung, X-A-ST, version 1, Enter Calculus Companion. Used for the signature and non-sourcing comparison. https://enter.grok.me/browse/X-A-ST.

CheungXBST

N. Cheung, X-B-ST: One scalar retarded map on the X-A-ST host, version 1, Enter Calculus Companion. Supported retained-shadow and equation/Hessian conventions. https://enter.grok.me/browse/X-B-ST.

CheungXCST

N. Cheung, X-C-ST: Second-order scalar completion on the inherited X-A-ST/X-B-ST host, version 1, Enter Calculus Companion. Support contract only; no higher product is imported. https://enter.grok.me/browse/X-C-ST.

CheungXIE

N. Cheung, XI-E, version 1, Enter Calculus Companion. Supplied excerpts :domain, :star. Product-domain versus state-selection distinction only. https://enter.grok.me/browse/XI-E.

CheungO1ST

N. Cheung, XVI-O1-ST, version 5, supplied identifier -O1-ST-v5.tex. Used for finite reporting and integrity-aware residual retention. No loop, phase reconciliation, or quantum closure is imported. https://enter.grok.me/browse/XVI-O1-ST.

CheungOai282A

N. Cheung, Oai282-A, version 1, Enter Calculus Companion. Supplied :coverage, :invisible. https://enter.grok.me/browse/Oai282-A.

CheungEn09

N. Cheung, En09-A, version 1, Enter Calculus Companion. Supplied destructive finite reporting and record–residual separation excerpts. https://enter.grok.me/browse/En09-A.

CheungXVIO

N. Cheung, Landmark XVI-O, supplied series status record. Read-only reference; no O.1 update is asserted. https://enter.grok.me/browse/XVI-O.

CheungXVIN

N. Cheung, Landmark XVI-N, supplied frozen prepared-source record. Not discharged by this scalar calculation. https://enter.grok.me/browse/XVI-N.

DocumentaryBoundary

N. Cheung, supplied excerpts from XIV-H, version 1; XIV-I, version 1; XIV-J, version 1; and XV-B, version 2. Used only to preserve the documentary non-transfer boundary: internal kernels and partial reference constructions do not constitute complete characteristic quantum admission. No graph-specific theorem is imported into the present scalar extension problem.