Boundaries in Field Theory |

**In General** > s.a. hamiltonian
dynamics; symplectic structures.

* __ Issues__: Choice of boundary terms in the action, or other functionals
such as conserved quantities, and boundary conditions for (bulk) field theories,
taking into account possible corner terms where the boundary
is not smooth and/or possible null portions of the boundary.

@ __Boundary dynamics__: Bordag et al PRD(02)ht/01 [Robin boundary conditions].

@ __Fields propagating across junctions__: Fomin & Shtanov CQG(02)ht/00;
> s.a. actions for general relativity; metric matching conditions.

@ __Boundary conditions__: Trautman BAPS(58)-a1604 [at infinity];
Galvan qp/98 [measure];
Wharton Sym(10)-a1003 + pirsa(09) [time-symmetric, and quantum foundations].

@ __Related topics__: Kheyfets & Wheeler IJTP(86)
[boundary of a boundary principle];
Zuber ht/00-ln [rational conformal field theory].

**Field Theories on Manifolds with Boundary** > s.a. ads-cft correspondence
[and Maldacena conjecture]; holography; topology.

@ __General references__: Barbero et al CQG(14)-a1306 [Hamiltonian and symplectic-Lagrangian descriptions];
Troessaert a1506 [canonical structure].

@ __Bulk / boundary relationship__: Balasubramanian et al PRD(99)ht/98 [anti-de Sitter space],
JHEP(00)ht;
Longo & Rehren RVMP(04)mp [boundary conformal field theory];
Hertog & Horowitz PRL(05)ht/04.

@ __Specific spacetimes__: Keski-Vakkuri PRD(99)ht/98 [BTZ black holes].

> __Examples__: see actions
for general relativity; BF theories; branes;
canonical general relativity; chern-simons theory;
dilaton; electromagnetism and in
curved spacetime; gauge theories; gravitational energy;
hamiltonian systems; parametrized theories;
quasilocal general relativity; supersymmetric field theories;
topological field theories.

**Boundaries in Quantum Field Theory** > s.a. klein-gordon theory;
QED; types of yang-mills theories.

@ __General references__: Solodukhin NPB(99)ht/98 [correlations and Green's functions];
Susskind & Witten ht/98 [holographic bound];
Giddings PRL(99)ht;
Esposito ht/00-proc [conceptual];
Oeckl PLB(03)ht [for quantum mechanics and quantum gravity];
Asorey et al JPA(06)
[space of boundary conditions for scalar quantum field theory];
Guo et al IJTP(08) [canonical quantization];
Ford & Svaiter PRD(09)-a0903 [fluid analog model];
Asorey & Muñoz-Castañeda IJGMP(12)-a1307 [effect on infrared behavior];
Govindarajan & Nair PRD(14) [instabilities];
Lowdon NPB(14)-a1408 [necessary and sufficient condition for arbitrary spatial boundary terms to vanish, and QCD example];
Asorey et al a1501
[charge conservation and properties of the space of physical boundary conditions];
Rehren a1601-proc [boundary condition classification].

@ __General-boundary formulation__: Oeckl ATMP(08)ht/05,
JPCS(07)ht/06;
Oeckl Sigma(12)-a1009 [holomorphic quantization of linear field theory];
Oeckl ATMP(15)-a1201 [Schrödinger-Feynman quantization];
> s.a. gauge theories; quantum statistical mechanics.

@ __Euclidean quantum field theory__: Esposito DMA-gq/95 [electromagnetism];
Conrady & Rovelli IJMPA(04)ht/03 ["general boundary" formulation].

@ __Gravity__: Esposito et al 97;
Wieland a1706 [boundary modes and discreteness of the area spectrum].

@ __Gauge theory__: Vassilevich PRD(95)gq/94 [QED];
Vassilevich PLB(98)ht/97 [Faddeev-Popov];
Esposito IJMPA(00)ht [boundary operators].

@ __Edge states__: John et al NPB(95) [and renormalization group];
Boschi-Filho & Braga PLB(02)ht/01 [field operators];
Asorey et al RVMP(16)-a1505 [and Robin boundary conditions];
Govindarajan & Tibrewala PRD(15)-a1506 [for the Dirac operator on manifolds with boundary];
Karabali & Nair PRD(15)-a1507 [boundary action for boundary conditions as bilocal dynamical fields];
Barbero et al CQG(17)-a1701 [boundary Hilbert spaces];
Hashimoto et al a1702 [edge-of-edge states, and condensed-matter physics].

@ __Algebraic approach__: Longo & Witten CMP(11)-a1004;
Nosari a1512-proc

@ __Types of quantum field theories__:
Bajnok et al NPB(05) [1+1 dimensions];
Haba AP(06) [with boundary/brane interaction];
Fosco et al PLB(10)-a0912 [with singular boundary interactions].

@ __Related topics__: Bajnok et al NPB(04)ht/03 [perturbative];
Elizalde JPA(03)ht [boundary conditions];
Bastianelli et al JHEP(07)ht/06 [worldline approach];
Fosco et al PRD(10)-a1011 [inertial forces and dissipation on accelerated boundaries];
> s.a. mirrors in quantum field theory.

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