Problems With Complex Actions

We consider Euclidean functional integrals involving actions which are not exclusively real. This situation arises, for example, when there are $t$-odd terms in the the Minkowski action. Writing the action in terms of only real fields (which is always possible), such terms appear as explicitly imaginary terms in the Euclidean action. The usual quanization procedure which involves finding the critical points of the action and then quantizing the spectrum of fluctuations about these critical points fails. In the case of complex actions, there do not exist, in general, any critical points of the action on the space of real fields, the critical points are in general complex. The proper definition of the function integral then requires the analytic continuation of the functional integration into the space of complex fields so as to pass through the complex critical points according to the method of steepest descent. We show a simple example where this procedure can be carried out explicitly. The procedure of finding the critical points of the real part of the action and quantizing the corresponding fluctuations, treating the (exponential of the) complex part of the action as a bounded integrable function is shown to fail in our explicit example, at least perturbatively.Comment: 6+epsilon pages, no figures, presented at Theory CANADA

Complex Monopoles in the Georgi-Glashow-Chern-Simons Model

We investigate the three dimensional Georgi-Glashow model with a Chern-Simons term. We find that there exist complex monopole solutions of finite action. They dominate the path integral and disorder the Higgs vacuum, but electric charges are not confined. Subtleties in the gauge fixing procedure in the path integral and issues related to Gribov copies are noted.Comment: 24 pages and 3 figures, Section 5 is extended,References adde

A Room-Temperature High-Conductivity Metal Printing Paradigm with Visible-Light Projection Lithography

Fabricating electronic devices require integrating metallic conductors and polymeric insulators in complex structures. Current metal-patterning methods such as evaporation and laser sintering require vacuum, multistep processes, and high temperature during sintering or postannealing to achieve desirable electrical conductivity, which damages low-temperature polymer substrates. Here reports a facile ecofriendly room-temperature metal printing paradigm using visible-light projection lithography. With a particle-free reactive silver ink, photoinduced redox reaction occurs to form metallic silver within designed illuminated regions through a digital mask on substrate with insignificant temperature change (<4 °C). The patterns exhibit remarkably high conductivity achievable at room temperature (2.4 × 107 S m−1, ≈40% of bulk silver conductivity) after simple room-temperature chemical annealing for 1–2 s. The finest silver trace produced reaches 15 µm. Neither extra thermal energy input nor physical mask is required for the entire fabrication process. Metal patterns were printed on various substrates, including polyethylene terephthalate, polydimethylsiloxane, polyimide, Scotch tape, print paper, Si wafer, glass coverslip, and polystyrene. By changing inks, this paradigm can be extended to print various metals and metal–polymer hybrid structures. This method greatly simplifies the metal-patterning process and expands printability and substrate materials, showing huge potential in fabricating microelectronics with one system

Injection therapy and denervation procedures for chronic low-back pain: a systematic review

Injection therapy and denervation procedures are commonly used in the management of chronic low-back pain (LBP) despite uncertainty regarding their effectiveness and safety. To provide an evaluation of the current evidence associated with the use of these procedures, a systematic review was performed. Existing systematic reviews were screened, and the Cochrane Back Review Group trial register was searched for randomized controlled trials (RCTs) fulfilling the inclusion criteria. Studies were included if they recruited adults with chronic LBP, evaluated the use of injection therapy or denervation procedures and measured at least one clinically relevant outcome (such as pain or functional status). Two review authors independently assessed studies for eligibility and risk of bias (RoB). A meta-analysis was performed with clinically homogeneous studies, and the GRADE approach was used to determine the quality of evidence. In total, 27 RCTs were included, 14 on injection therapy and 13 on denervation procedures. 18 (66%) of the studies were determined to have a low RoB. Because of clinical heterogeneity, only two comparisons could be pooled. Overall, there is only low to very low quality evidence to support the use of injection therapy and denervation procedures over placebo or other treatments for patients with chronic LBP. However, it cannot be ruled out that in carefully selected patients, some injection therapy or denervation procedures may be of benefit