Quantum Reflection as a New Signature of the Quantum Vacuum Nonlinearity Nico Seegert TPI Uni Jena & Helmholtz-Institut Jena February 4th, 2014 Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Contents Properties of the Quantum Vacuum 1 Photon Propagation in Inhomogeneous Fields 2 Quantum Reflection 3 Time-independent, one-dimensional Inhomogeneity 4 Outlook: Time-dependent Inhomogeneities 5 Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Light Propagation in Vacuum Classical vacuum is empty Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Light Propagation in Vacuum Classical vacuum is empty Light propagation in vacuum governed by (linear) Maxwell equations ∂ µ F µν = 0 → superposition principle Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Light Propagation in Vacuum QED vacuum : Zero-point energy fluctuations Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Light Propagation in Vacuum Real electromagnetic fields couple to e − e + -loops = ⇒ Nonlinear interactions F µν Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Heisenberg-Euler Effective Action First quantitative description: Heisenberg-Euler Lagrangian (1936) Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Heisenberg-Euler Effective Action First quantitative description: Heisenberg-Euler Lagrangian (1936) 1-loop effective action Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Heisenberg-Euler Effective Action First quantitative description: Heisenberg-Euler Lagrangian (1936) 1-loop effective action Valid for “locally” constant EM-fields F µν � 3 . 9 × 10 − 13 m m ∼ Scales: λ = 1 = 1 . 3 × 10 − 21 s Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Heisenberg-Euler Effective Action First quantitative description: Heisenberg-Euler Lagrangian (1936) 1-loop effective action Valid for “locally” constant EM-fields F µν � 3 . 9 × 10 − 13 m m ∼ Scales: λ = 1 = 1 . 3 × 10 − 21 s Critical field strengths: = m 2 � E cr � � 1 . 3 × 10 18 V / m � ∼ = 4 . 4 × 10 9 T B cr e Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Heisenberg-Euler Effective Action First quantitative description: Heisenberg-Euler Lagrangian (1936) 1-loop effective action Valid for “locally” constant EM-fields F µν � 3 . 9 × 10 − 13 m m ∼ Scales: λ = 1 = 1 . 3 × 10 − 21 s Critical field strengths: = m 2 � E cr � � 1 . 3 × 10 18 V / m � ∼ = 4 . 4 × 10 9 T B cr e Splitting of F µν = F µν + f µν , with F µν ≫ f µν and F µν = const. Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Optical Signatures of the Quantum Vacuum Nonlinear interactions between probe photons and electromagnetic background field: ∝ ( f µν ) 2 Magnetic birefringence (Toll’52) Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Optical Signatures of the Quantum Vacuum Nonlinear interactions between probe photons and electromagnetic background field: ∝ ( f µν ) 3 ∝ ( f µν ) 2 Magnetic birefringence Photon splitting (Adler’71) (Toll’52) Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Optical Signatures of the Quantum Vacuum Nonlinear interactions between probe photons and electromagnetic background field: ∝ ( f µν ) 3 ∝ ( f µν ) 2 Magnetic birefringence Photon splitting (Adler’71) (Toll’52) ∝ ( f µν ) 4 Light-by-light scattering (Karplus’51) Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Optical Signatures of the Quantum Vacuum Nonlinear interactions between probe photons and electromagnetic background field: ∝ ( f µν ) 3 ∝ ( f µν ) 2 Magnetic birefringence Photon splitting (Adler’71) (Toll’52) ∝ ( f µν ) 4 Pair production Light-by-light scattering (Sauter’31,HE’35,Schwinger’51) (Karplus’51) Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Optical Signatures of the Quantum Vacuum This talk : Introduction of a new optical signature related to photon propagation Quantum vacuum modified by background field = effective potential for probe photons Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Optical Signatures of the Quantum Vacuum This talk : Introduction of a new optical signature related to photon propagation Quantum vacuum modified by background field = effective potential for probe photons “Quantum Vacuum Reflection” Reflection of probe photons at a strong electromagnetic background field Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Properties of the Quantum Vacuum Optical Signatures of the Quantum Vacuum This talk : Introduction of a new optical signature related to photon propagation Quantum vacuum modified by background field = effective potential for probe photons “Quantum Vacuum Reflection” Reflection of probe photons at a strong electromagnetic background field Requires manifestly k ′ , ω ′ k , ω inhomogeneous background field → energy/momentum transfer Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Photon Propagation in Inhomogeneous Fields Outline 1 Properties of the Quantum Vacuum Photon Propagation in Inhomogeneous Fields 2 Quantum Reflection 3 Time-independent, one-dimensional Inhomogeneity 4 Outlook: Time-dependent Inhomogeneities 5 Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Photon Propagation in Inhomogeneous Fields Effective Action and Equations of Motion Generalized effective action for photon propagation in a slowly varying electromagnetic background field: (cf. Dittrich,Gies’00) Γ[ a ] = − 1 � � − 1 � d 4 x F µν F µν d 4 x d 4 y a µ ( x )Π µν ( x, y | A ) a ν ( y ) � � 4 2 � a + A Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Photon Propagation in Inhomogeneous Fields Effective Action and Equations of Motion Generalized effective action for photon propagation in a slowly varying electromagnetic background field: (cf. Dittrich,Gies’00) Γ[ a ] = − 1 � � − 1 � d 4 x F µν F µν d 4 x d 4 y a µ ( x )Π µν ( x, y | A ) a ν ( y ) � � 4 2 � a + A with the “photon polarization tensor” in an electromagnetic background field at one loop order µ ν Π µν ( x, y | A ) = Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Photon Propagation in Inhomogeneous Fields Effective Action and Equations of Motion Generalized effective action for photon propagation in a slowly varying electromagnetic background field: (cf. Dittrich,Gies’00) Γ[ a ] = − 1 � � − 1 � d 4 x F µν F µν d 4 x d 4 y a µ ( x )Π µν ( x, y | A ) a ν ( y ) � � 4 2 � a + A with the “photon polarization tensor” in an electromagnetic background field at one loop order µ ν Π µν ( x, y | A ) = Equations of Motion ( k 2 g µν − k µ k ν ) a ν ( k ) = − d 4 k ′ (2 π ) 4 ˜ Π µν ( k, − k ′ | A ) a ν ( k ′ ) � Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Photon Propagation in Inhomogeneous Fields The Photon Polarization Tensor Explicit expressions for the photon polarization tensor in momentum space have been obtained at (Batalin,Shabad’71) one loop order, for arbitrary constant electromagnetic fields involving external couplings to all orders . Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
Photon Propagation in Inhomogeneous Fields The Photon Polarization Tensor Explicit expressions for the photon polarization tensor in momentum space have been obtained at (Batalin,Shabad’71) one loop order, for arbitrary constant electromagnetic fields involving external couplings to all orders . Here: Purely magnetic case Π µν ( x, x ′ | B ) = Π µν ( x − x ′ | B ) Π µν ( k | B ) ← → Advances in Strong-Field Electrodynamics @ Eötvös University, Budapest, Feb.4th 2014
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