I study the response of a particle detector coupled to quantized massless complex scalar field in four dimensional Minkowski spacetime through nonlinear Lagrangian. I find that as in the real scalar field： the partic...I study the response of a particle detector coupled to quantized massless complex scalar field in four dimensional Minkowski spacetime through nonlinear Lagrangian. I find that as in the real scalar field： the particle detector will not respond when it is in inertial motion; If accelerated in its own frame reference, it does respond and feel the same temperature. But different from the real scalar field case, the detector＇s transition amplitude is concerned with particle-antiparticle creation, and the response of the detector is （1/α^2 ＋ ε^2）/24π^2 times of that in real scalar field, with 1/α the accelerator of the detector and e the energy gap between the detector＇s two energy level. It is due to the nonlinear property of the coupling Lagrangian. Whether the total charge of the system constructed by the particle detector and vacuum is conserved is also considered and analyzed.展开更多
Einstein claimed that one cannot de？ne global time, and in order to formulate physical dynamics, it is useful to adopt ？ber bundle structure. We de？ne topological space E which consists of base space X and ？bers ...Einstein claimed that one cannot de？ne global time, and in order to formulate physical dynamics, it is useful to adopt ？ber bundle structure. We de？ne topological space E which consists of base space X and ？bers F = Π-1（X）, where Π is a projection of an event on the base space. Relations between initial data and ？nal data are de？ned by group G and a Fiber bundle is de？ned as as set （E, Π, F, G, X）.Tangent bundle TX of real linear space X is de？ned by the projection πTX = TX → X; （x,a） → a for any a ∈ X and a sphere Sn any non negative integer n may be thought to be a smooth submanifold of Rn＋1 and TSn is identi？ed as {（x,a） ∈Rn＋1 ×Sn ： x·a = 0} Connes proposed that when one adopts non-commutative geometry, one can put two ？bers at each point of X and on top of the two ？bers de？ne the initial input event and the ？nal detection event. When one considers dynamics of leptons de？ned by Dirac equation, group G is given by quaternions H, and the base space X is usually taken to be S3. E. Cartan studied dynamics of spinors which are described by octonions or Cayley numbers which is an ordered product of two quaternions. The asymptotic form Y of this system is S7. Cayley numbers of S7 are de？ned as a 3-sphere bundle over S4 with group S3. Therefore in T X there are two manifolds S3 × R4 and S3＇ × R4 and the direction of propagation of time on S3 and S＇3 are not necessarily same. We apply this formulation to experimentally observed violation of time reversal symmetry in pp→ tt process and for understanding the result of time reversal based nonlinear elastic wave spectroscopy （TR-NEWS） in memoducers.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10947016
文摘I study the response of a particle detector coupled to quantized massless complex scalar field in four dimensional Minkowski spacetime through nonlinear Lagrangian. I find that as in the real scalar field： the particle detector will not respond when it is in inertial motion; If accelerated in its own frame reference, it does respond and feel the same temperature. But different from the real scalar field case, the detector＇s transition amplitude is concerned with particle-antiparticle creation, and the response of the detector is （1/α^2 ＋ ε^2）/24π^2 times of that in real scalar field, with 1/α the accelerator of the detector and e the energy gap between the detector＇s two energy level. It is due to the nonlinear property of the coupling Lagrangian. Whether the total charge of the system constructed by the particle detector and vacuum is conserved is also considered and analyzed.
文摘Einstein claimed that one cannot de？ne global time, and in order to formulate physical dynamics, it is useful to adopt ？ber bundle structure. We de？ne topological space E which consists of base space X and ？bers F = Π-1（X）, where Π is a projection of an event on the base space. Relations between initial data and ？nal data are de？ned by group G and a Fiber bundle is de？ned as as set （E, Π, F, G, X）.Tangent bundle TX of real linear space X is de？ned by the projection πTX = TX → X; （x,a） → a for any a ∈ X and a sphere Sn any non negative integer n may be thought to be a smooth submanifold of Rn＋1 and TSn is identi？ed as {（x,a） ∈Rn＋1 ×Sn ： x·a = 0} Connes proposed that when one adopts non-commutative geometry, one can put two ？bers at each point of X and on top of the two ？bers de？ne the initial input event and the ？nal detection event. When one considers dynamics of leptons de？ned by Dirac equation, group G is given by quaternions H, and the base space X is usually taken to be S3. E. Cartan studied dynamics of spinors which are described by octonions or Cayley numbers which is an ordered product of two quaternions. The asymptotic form Y of this system is S7. Cayley numbers of S7 are de？ned as a 3-sphere bundle over S4 with group S3. Therefore in T X there are two manifolds S3 × R4 and S3＇ × R4 and the direction of propagation of time on S3 and S＇3 are not necessarily same. We apply this formulation to experimentally observed violation of time reversal symmetry in pp→ tt process and for understanding the result of time reversal based nonlinear elastic wave spectroscopy （TR-NEWS） in memoducers.
