Memory effects and the related infrared physics Sotaro Sugishita (Osaka Univ.) Strings and Fields 2018 YITP, July 30, 2018
Based on: Yuta Hamada & SS, JHEP 1711 (2017) 203 [arXiv:1709.05018] Yuta Hamada & SS, JHEP 1807 (2018) 017 [arXiv:1803.00738] Hayato Hirai & SS, JHEP 1807 (2018) 122 [arXiv:1805.05651] Next speaker
Gravitational Waves Detected! GW150914 https://www.ligo.c altech.edu/image/ ligo20160211a
[Nature 327, 123 – 125 (1987)] from Physics-Uspekhi 55(1)109-110 (2012) from Nobelprize.org
[Nature 327, 123 – 125 (1987)] from Physics-Uspekhi 55(1)109-110 (2012) from Nobelprize.org
Gravitational memory effect [ Zel’dovich & Polnarev (1974)] Gravitational wave burst w/ finite duration detector GW source • Detector consists of two free test particles. GW passes before after
Gravitational memory effect [ Zel’dovich & Polnarev (1974)] Gravitational wave burst w/ finite duration detector GW source • Detector consists of two free test particles. GW passes before after permanent displacement of test particles Memory effect
Physics in asymptotically flat space detector Isolated source. GW Detector is far away from the source. source • Long-distance behaviors of gravitational waves in asymptotically flat spacetime. soft theorem related to asymptotic symmetry
IR Triangular Relation [Strominger (2013), … ] Memory Effect Soft Asymptotic Theorem Symmetry
Each corner is not new. Gravitational Memory Effect Zel’dovich & Polnarev (1974) Soft Photon Theorem & Soft Graviton Theorem Low (1954), Gell-Mann & Goldberger (1954), Weinberg (1965) Asymptotic Symmetry (BMS symmetry) Bondi, van der Burg & Metzner (1962), Sachs (1962) The relations among them are somewhat new. [Strominger (2013), … ]
Massless radiation • Linearized gravitational eq. [cf. Nonlinear memory, Christodoulou (1991),Thorne (1992)]
Massless radiation • Linearized gravitational eq. [cf. Nonlinear memory, Christodoulou (1991),Thorne (1992)] Other massless radiations satisfy almost the same eq. • Electromagnetic wave • Scalar wave
Massless radiation • Linearized gravitational eq. [cf. Nonlinear memory, Christodoulou (1991),Thorne (1992)] Other massless radiations satisfy almost the same eq. • Electromagnetic wave EM memory effect [Bieri & Garfinkle (2013), Tolish & Wald (2014), Susskind (2015)] • Scalar wave Scalar memory effect [Tolish & Wald (2014), Hamada & SS (2017)]
Excuse me Electromagnetism is probably simpler than gravity. Maxwell’s eq. is easier than Einstein’s eq . Let’s consider the electromagnetism for a while, though I was asked to give a talk about gravitational memory.
Excuse me Electromagnetism is probably simpler than gravity. Maxwell’s eq. is easier than Einstein’s eq . Let’s consider the electromagnetism for a while, though I was asked to give a talk about gravitational memory. Klein-Gordon is much easier.
Excuse me Electromagnetism is probably simpler than gravity. Maxwell’s eq. is easier than Einstein’s eq . Let’s consider the electromagnetism for a while, though I was asked to give a talk about gravitational memory. Klein-Gordon is much easier. But, the relation of scalar memory to symmetry is not so clear…. [Campiglia, Coito & Mizera (2017)]
Outline Introduction Memory effect in electromagnetism Relation to soft theorem Some comments
Memory effect as charge conservation Electromagnetic memory effect EM radiation with the change of the asymptotic behaviors of EM field. like This change is the memory, which is related to (or memorize) the change of the configurations of the source (charged objects).
Memory effect as charge conservation Electromagnetic memory effect EM radiation with the change of the asymptotic behaviors of EM field. like This change is the memory, which is related to (or memorize) the change of the configurations of the source (charged objects). We derive the electromagnetic memory effect from the conservation laws associated with the asymptotic symmetry for classical systems. [Hirai & SS (2018)]
Setup scattering of charged particles Assume that charged particles behave as free particles except for a small scattering region. cf. [Laddha and Sen (2018)] Maxwell’s eq. Consider the solution from large- 𝑠 region.
Gauge charge Initially and finally, charged particles move at constant velocities (in our assumption).
Gauge charge Initially and finally, charged particles move at constant velocities (in our assumption). • electric flux integral with parameter arbitrary function If = const.,
Gauge charge Take the surface as two-sphere with radius 𝑆 at past or future infinity, and set the radius 𝑆 → ∞ . (The precise definition will be given later.) initial final
Gauge charge conservation? initial final If = const., from the total electric charge conservation, For general , This change implies the EM radiation with a memory.
Easy example A static charge at Ԧ 𝑦 0 suddenly moves with velocity Ԧ 𝑤 at time 𝑢 0 . The retarded potential: outside of future light cone
Easy example In the Lorenz gauge, shift outside of We use the retarded coordinates future light cone to see this shift in large 𝑠 .
Easy example retarded coordinates Future null infinity
Easy example retarded coordinates Future null infinity two angular components. DOF of EM waves. (cf. TT comp. of GW) memory
Memory formula This memory knows information of charges. It satisfies : arbitrary function on 𝑇 2
Memory formula This memory knows information of charges. It satisfies : arbitrary function on 𝑇 2 The formula holds for more general scatterings.
Memory formula This memory knows information of charges. It satisfies : arbitrary function on 𝑇 2 The formula holds for more general scatterings. It can be derived from the charge conservation of the large gauge transformation.
Memory formula This memory knows information of charges. It satisfies : arbitrary function on 𝑇 2 The formula holds for more general scatterings. It can be derived from the charge conservation of the large gauge transformation. e.g. global U(1) trsf. = const., total electric charge consv.
Large gauge transformation We use the Lorenz gauge “Large gauge transformations” in this talk mean residual gauge trsfs in the Lorenz gauge, which satisfy and behave as near .
Large gauge transformation We use the Lorenz gauge “Large gauge transformations” in this talk mean residual gauge trsfs in the Lorenz gauge, which satisfy and behave as near . Such gauge parameters are given by [Campiglia & Laddha (2015)] near is the antipodal pt of
Gauge current conservation • conserved current for the gauge transformation w/ :
Gauge current conservation • conserved current for the gauge transformation w/ : 𝑊 is surrounded by 5 surfaces.
Gauge current conservation • conserved current for the gauge transformation w/ : 𝑊 is surrounded by 5 surfaces.
Gauge current conservation • conserved current for the gauge transformation w/ : 𝑊 is surrounded by 5 surfaces. Take the limit 𝑈 → ∞ memory formula
Charge on null surface Let’s first consider the surface on null surface:
Charge on null surface Let’s first consider the surface on null surface: • Massive particles cannot reach . • Only angular comps of gauge field survive.
Charge on null surface Let’s first consider the surface on null surface: • Massive particles cannot reach . • Only angular comps of gauge field survive. L.H.S of memory formula
No initial radiation In our setup, there is no initial radiation
Charge on timelike infinity Gauge charges in balls Σ 𝑔/𝑗 for matter currents and their Lienard-Wiecherd potentials.
Large gauge current conservation: So far,
Large gauge current conservation: So far,
Large gauge current conservation: So far,
Large gauge current conservation: So far,
Charge on spacelike infinity electric fields created by charged particles before scatterings
Charge on spacelike infinity electric fields created by charged particles before scatterings The integrand does not decay for the large gauge parameter.
Charge on spacelike infinity electric fields created by charged particles before scatterings The integrand does not decay for the large gauge parameter. antipodal
Antipodal matching [He, Mitra, Porfyriadis & Strominger (2014)] Electric fields also satisfy the antipodal matching condition.
Antipodal matching [He, Mitra, Porfyriadis & Strominger (2014)] Electric fields also satisfy the antipodal matching condition.
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